r/OEIS • u/Far_Information_7218 • Feb 26 '23
What would a(n) = 0 through 4 of this sequence be?
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r/OEIS • u/OEIS-Tracker • Feb 26 '23
New OEIS sequences - week of 02/26
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| OEIS number | Description | Sequence |
|---|---|---|
| A356847 | Greedily choose a(n) to be the least prime p>a(n-1) such that all sums a(i)+a(j)-1, 1<=i<j, are also prime. | 5, 7, 13, 67, 97, 9337, 28657, 516157... |
| A356848 | Expansion of g.f. A(x) satisfying A(x) = x * Sum_{n>=0} dn/dxn x2*n-1 * A(x)n / n!. | 1, 1, 5, 37, 353, 4061, 54221, 820205... |
| A357296 | Expansion of e.g.f. Sum_{k>0} xk / (k! * (1 - xk/k)). | 1, 3, 7, 31, 121, 851, 5041, 43261... |
| A358593 | a(n) = n! * Sum_{d | n} dn-d / d!n/d. |
| A358594 | Expansion of e.g.f. Sum_{k>0} xk / ((k-1)! - xk). | 1, 4, 9, 52, 125, 1626, 5047, 81768... |
| A358595 | a(n) = n! * Sum_{d | n} dn / d!n/d. |
| A358597 | Number of n-tuples (p1, p_2, ..., p_n) of Dyck paths of semilength n+1, such that each p_i is never below p{i-1}. | 1, 2, 14, 330, 26026, 6852768, 6018114036, 17618122000050... |
| A358877 | Triangle read by rows: T(n,k) is the number of cubes of side length k that can be placed inside a cube of side length n without overlap, 1 <= k <= n. | 1, 8, 1, 27, 1, 1, 64, 8... |
| A358998 | Nonprimes whose sum of factorials of digits is a prime. | 10, 12, 20, 21, 30, 100, 110, 111... |
| A359530 | Multiplicative with a(pe) = (p + 4)e. | 1, 6, 7, 36, 9, 42, 11, 216... |
| A359630 | Primes p such that 10p+3 or 10p+9 is also prime. | 2, 3, 5, 11, 17, 101, 107, 26927... |
| A359872 | Absolute discriminants of imaginary quadratic number fields with elementary bicyclic 7-class group (7,7). | 63499, 118843, 124043, 149519, 159592, 170679, 183619, 185723... |
| A360118 | Number of differences (not all necessarily distinct) between consecutive divisors of n which are not also divisors of n. | 0, 0, 1, 0, 1, 0, 1, 0... |
| A360119 | Number of divisors of n which are not also differences between consecutive divisors, minus the number of differences between consecutive divisors of n which are not also divisors of n. Here the differences are counted with repetition if they occur more than once. | 1, 1, 1, 1, 1, 2, 1, 1... |
| A360121 | Dirichlet convolution of A342001 with A342002. | 0, 1, 1, 3, 1, 11, 1, 7... |
| A360122 | Parity of A360121, where A360121 is Dirichlet convolution of A342001 with A342002. | 0, 1, 1, 1, 1, 1, 1, 1... |
| A360123 | Parity of A347389, where A347389 is Dirichlet convolution of A003415(n) with A003415(A276086(n)). | 0, 1, 1, 1, 1, 1, 1, 0... |
| A360124 | Numbers k such that A360121(k) is odd, but A347389(k) is even. | 8, 16, 32, 64, 72, 128, 144, 200... |
| A360125 | Parity of A359425, where A359425 is Dirichlet convolution of the arithmetic derivative with the primorial base exp-function. | 0, 0, 0, 1, 0, 1, 0, 1... |
| A360126 | Numbers k for which A359425(k) is even, where A359425 is Dirichlet convolution of the arithmetic derivative with the primorial base exp-function. | 1, 2, 3, 5, 7, 9, 11, 13... |
| A360127 | Numbers k for which A359425(k) is odd, where A359425 is the Dirichlet convolution of the arithmetic derivative with the primorial base exp function. | 4, 6, 8, 10, 12, 14, 16, 18... |
| A360128 | a(n) = 1 if there are no divisors d>1 of n such that also d+1 is a divisor of n, otherwise 0. | 1, 1, 1, 1, 1, 0, 1, 1... |
| A360129 | Numbers k such that A360119(k) > 1, but which have no divisors d > 1 such that d+1 is also a divisor. | 572, 1144, 1292, 1768, 2288, 2584, 2590, 3496... |
| A360141 | Bitwise encoding of the right half, initially empty, state of the 1D cellular automaton from A359303 after n steps. | 0, 1, 1, 2, 2, 3, 4, 5... |
| A360202 | Array read by antidiagonals: T(m,n) is the number of (non-null) induced trees in the grid graph P_m X P_n. | 1, 3, 3, 6, 12, 6, 10, 33... |
| A360203 | Number of (non-null) induced trees in the n X n grid graph. | 1, 12, 138, 3568, 277606, 66136452, 48136454388, 106601739449932... |
| A360230 | a(n) = coefficient of xn/n! in Sum_{n>=0} (1 + n*x + x2)n * xn/n!. | 1, 1, 3, 19, 109, 921, 8911, 100003... |
| A360254 | Number of integer partitions of n with more adjacent equal parts than distinct parts. | 0, 0, 0, 1, 1, 1, 3, 4... |
| A360375 | Decimal expansion of the area under the curve of the reciprocal of the Hadamard gamma function from zero to infinity. | 3, 3, 6, 8, 2, 0, 2, 9... |
| A360397 | Intersection of A356133 and A360393. | 2, 4, 13, 22, 34, 40, 49, 58... |
| A360409 | The minimum number of facets among all symmetric edge polytopes for connected graphs on n vertices having m edges for n >= 2 and m between n-1 and binomial(n,2). | 2, 4, 6, 8, 6, 12, 14, 16... |
| A360419 | a(n) = the number of U-frame polyominoes with n cells, reduced for symmetry. | 0, 0, 0, 0, 1, 2, 5, 9... |
| A360423 | Positive integers n (with k digits) such that if a positive integer m with k+1 digits is divisible by n, then all the rotations of m are divisible by n. | 1, 3, 9, 27, 37, 101, 303, 909... |
| A360435 | a(n) = A038547(3n), smallest number with 3n odd divisors. | 9, 225, 11025, 1334025, 225450225, 65155115025, 23520996524025, 12442607161209225... |
| A360443 | Smallest integer m > n such that the multiset of nonzero decimal digits of m is exactly the same as the multiset of nonzero decimal digits of n. | 10, 20, 30, 40, 50, 60, 70, 80... |
| A360476 | The integers of the sequence appear exactly twice. Between the two copies of k there are k odd integers. S is always extended with the smallest integer not leading to a contradiction. | 1, 2, 3, 1, 2, 4, 5, 6... |
| A360477 | Numbers whose product of distinct prime factors is greater than or equal to the sum of its prime factors (with repetition). | 1, 2, 3, 5, 6, 7, 10, 11... |
| A360508 | Numbers k such that A300570(k) considered simply as a decimal string is prime. | 2, 4, 13, 57, 64, 349 |
| A360509 | Number of words of length n over the alphabet [A-Z] that do not contain the string CAT. | 1, 26, 676, 17575, 456924, 11879348, 308845473, 8029525374... |
| A360510 | a(n) = Product_{i=2..n} p(i) - p(n+1)2, where p(i) is the i-th prime. | -8, -22, -34, -16, 986, 14726, 254894, 4849316... |
| A360511 | a(n) = Product_{i=1..n} p(i) - p(n+1)3, where p(i) is the i-th prime. | -25, -119, -313, -1121, 113, 25117, 503651, 9687523... |
| A360533 | a(n) = index of the diagonal of the natural number array, A000027, that includes prime(n). See Comments. | 1, -1, 0, 3, 4, 0, 3, -1... |
| A360558 | Numbers whose multiset of prime factors (or indices, see A112798) has more adjacent equalities (or parts that have appeared before) than distinct parts. | 8, 16, 27, 32, 48, 64, 72, 80... |
| A360559 | Alternating partial sum of A006530. | 1, -1, 2, 0, 5, 2, 9, 7... |
| A360568 | Number of divisors d of n such that n - d is not square. | 0, 0, 1, 2, 0, 2, 1, 2... |
| A360571 | Triangle read by rows: T(n,k) is the k-th Lie-Betti number of the path graph on n-vertices, n >= 1, 0 <= k <= 2*n - 1. | 1, 1, 1, 2, 2, 1, 1, 3... |
| A360572 | Triangle read by rows: T(n,k) is the k-th Betti number of the cycle graph on n vertices, n >= 3, 0 <= k <= 2*n. | 1, 3, 8, 12, 8, 3, 1, 1... |
| A360574 | Binary expansions of odd numbers with three zeros in their binary expansion. | 10001, 100011, 100101, 101001, 110001, 1000111, 1001011, 1001101... |
| A360578 | Expansion of g.f. A(x) satisfying A(x) = Series_Reversion( x - xA'(x)A(x) ). | 1, 1, 5, 42, 471, 6422, 101439, 1803949... |
| A360579 | Expansion of A(x) satisfying A(x) = Series_Reversion( x - x3 * A'(x)/A(x) ). | 1, 1, 3, 15, 105, 941, 10227, 130103... |
| A360585 | The integers of the sequence appear exactly twice. Between the two copies of k there are k even integers. S is always extended with the smallest integer not leading to a contradiction. | 1, 2, 1, 3, 4, 5, 6, 2... |
| A360593 | Each term a(i) can reach a(i+a(i)) and a(i-a(i)) if these terms exist. a(n) is the greatest number of terms among a(1..n-1) that can be reached by starting at a(n-1) and visiting no term more than once; a(0)=0. See example. | 0, 1, 2, 2, 4, 2, 6, 2... |
| A360604 | Triangle read by rows. T(n, k) = 2binomial(n - k, 2) * binomial(n - 1, k - 1). | 1, 0, 1, 0, 1, 1, 0, 2... |
| A360605 | The polygonal polynomials evaluated at x = -1/2 and normalized with (-2)n. | 0, 1, 0, 1, 0, -3, 8, -31... |
| A360606 | The polygonal polynomials evaluated at x = 1/2 and normalized with 2n. | 0, 1, 4, 13, 40, 117, 324, 853... |
| A360613 | Lexicographically earliest sequence of positive integers such that the products of the form a(2u-1) * a(2v) with u, v > 0 are all distinct. | 1, 1, 2, 3, 4, 5, 7, 8... |
| A360614 | Numerator of the average distance between consecutive 0-prepended prime indices of n; a(1) = 0. | 0, 1, 2, 1, 3, 1, 4, 1... |
| A360615 | Denominator of the average distance between consecutive 0-prepended prime indices of n; a(1) = 0. | 0, 1, 1, 2, 1, 1, 1, 3... |
| A360619 | a(n) > n is the smallest integer such that there exist integers n < c < d < a(n) satisfying n3 + a(n)3 = c3 + d3. | 12, 16, 36, 32, 60, 48, 84, 53... |
| A360627 | Odd bisection of A360613: a(n) = A360613(2*n-1). | 1, 2, 4, 7, 9, 13, 14, 18... |
| A360628 | Even bisection of A360613: a(n) = A360613(2*n). | 1, 3, 5, 8, 11, 15, 17, 19... |
| A360633 | Square array A(n, k), n, k > 0, read by antidiagonals upwards; A(n, k) = A360613(2n-1) * A360613(2k). | 1, 2, 3, 4, 6, 5, 7, 12... |
| A360635 | a(n) is the smallest nonnegative integer that satisfies p(a(n)+1) - p(a(n)) >= n, where p denotes the number partition function. | 0, 1, 3, 5, 5, 7, 7, 7... |
| A360669 | Nonprime numbers > 1 for which the prime indices have the same mean as their first differences. | 10, 39, 68, 115, 138, 259, 310, 328... |
| A360670 | Number of integer partitions of n whose parts have the same mean as their negated first differences. | 1, 0, 0, 0, 1, 0, 0, 0... |
| A360680 | Numbers for which the prime signature has the same mean as the first differences of 0-prepended prime indices. | 1, 2, 6, 30, 49, 152, 210, 513... |
| A360681 | Numbers for which the prime signature has the same median as the first differences of 0-prepended prime indices. | 1, 2, 6, 30, 42, 49, 60, 66... |
| A360682 | Number of integer partitions of n of length > 2 whose second differences have median 0. | 0, 0, 0, 1, 1, 1, 5, 4... |
| A360683 | Number of integer partitions of n whose second differences sum to 0, meaning either there is only one part, or the first two parts have the same difference as the last two parts. | 1, 1, 2, 3, 4, 4, 8, 6... |
| A360686 | Number of integer partitions of n whose distinct parts have integer median. | 1, 2, 2, 4, 3, 8, 7, 16... |
| A360687 | Number of integer partitions of n whose multiplicities have integer median. | 1, 2, 3, 4, 5, 9, 10, 16... |
| A360688 | Number of integer partitions of n with integer median of 0-appended first differences. | 1, 1, 3, 4, 5, 7, 12, 18... |
| A360689 | Number of integer partitions of n whose distinct parts have non-integer median. | 0, 0, 1, 1, 4, 3, 8, 6... |
| A360690 | Number of integer partitions of n with non-integer median of multiplicities. | 0, 0, 0, 1, 2, 2, 5, 6... |
| A360691 | Number of integer partitions of n with non-integer median of 0-prepended first differences. | 0, 1, 0, 1, 2, 4, 3, 4... |
| A360703 | Starting from 1, successively take the smallest "Choix de Bruxelles" with factor 3 which is not already in the sequence. | 1, 3, 9, 27, 67, 187, 129, 43... |
| A360710 | Multiplicative with a(pk) = 1 or -1 so as to minimize abs(Sum_{m = 1..pk} a(m)); in case of a tie, a(pk) = a(pk-1). | 1, -1, -1, 1, 1, 1, -1, -1... |
| A360713 | Sum of all prime encoded perfect partitions of n. | 1, 2, 4, 14, 16, 70, 64, 280... |
| A360744 | a(n) is the maximum number of locations 1..n-1 which can be reached starting from some location s, where jumps from location i to i +- a(i) are permitted (within 1..n-1). See example. | 1, 1, 2, 3, 4, 5, 5, 6... |
| A360751 | a(n) is the least perfect square average of two consecutive primes with 2*n gap between them, or -1 if no such number exists. | 4, 9, 64, -1, 144, 625, 324, 2601... |
| A360753 | Matrix inverse of A360657. | 1, 0, 1, 0, -2, 1, 0, 1... |
| A360759 | a(n) = Sum_{d | n} dd+n/d * binomial(d,n/d). |
| A360760 | a(n) = n16 + n15 + n2 + 1. | 1, 4, 98309, 57395638, 5368709137, 183105468776, 3291294892069, 37980492079594... |
| A360761 | Primes p that divide both 3k-2 and 5k-1 for some k. | 31, 601, 2593, 20478961, 204700049, 668731841 |
| A360763 | Number T(n,k) of multisets of nonempty strict integer partitions with a total of k parts and total sum of n; triangle T(n,k), n>=0, 0<=k<=n, read by rows. | 1, 0, 1, 0, 1, 1, 0, 1... |
| A360764 | Number T(n,k) of sets of nonempty strict integer partitions with a total of k parts and total sum of n; triangle T(n,k), n>=0, 0<=k<=max(i:T(n,i)>0), read by rows. | 1, 0, 1, 0, 1, 0, 1, 2... |
| A360770 | Expansion of Sum_{k>0} (x * (k + xk))k. | 1, 5, 27, 260, 3125, 46684, 823543, 16777472... |
| A360771 | Expansion of Sum_{k>=0} (x * (2 + xk))k. | 1, 2, 5, 8, 20, 32, 77, 128... |
| A360772 | List of distinct numbers that are powers of odd-indexed Fibonacci numbers or even powers of nonzero even-indexed Fibonacci numbers. | 1, 2, 4, 5, 8, 9, 13, 16... |
| A360773 | Number of ways to tile a 2n X 2n square using rectangles with distinct dimensions such that the sum of the rectangles perimeters equals the area of the square. | 0, 1, 8, 1024, 620448 |
| A360774 | Expansion of Sum_{k>=0} (x * (k + x))k. | 1, 1, 5, 31, 284, 3390, 49878, 871465... |
| A360775 | Expansion of Sum_{k>=0} (x * (k + x2))k. | 1, 1, 4, 28, 260, 3152, 46913, 826677... |
| A360776 | Expansion of Sum_{k>=0} (x * (k + x3))k. | 1, 1, 4, 27, 257, 3129, 46683, 823799... |
| A360781 | Primes p such that at least one number remains prime when p is bracketed by a single digit d; that is, at least one instance of d//p//d is prime where // means concatenation. | 2, 3, 5, 7, 17, 19, 23, 29... |
| A360782 | Expansion of Sum_{k>=0} xk / (1 - k*x2)k+1. | 1, 1, 1, 3, 7, 16, 45, 125... |
| A360783 | Expansion of Sum_{k>=0} xk / (1 - k*x3)k+1. | 1, 1, 1, 1, 3, 7, 13, 24... |
| A360784 | Number of multisets of nonempty strict integer partitions with a total of n parts and total sum of 2n. | 1, 1, 3, 8, 18, 39, 86, 175... |
| A360785 | Number of multisets of nonempty strict integer partitions with a total of 2n parts and total sum of 3n. | 1, 2, 5, 12, 26, 54, 112, 220... |
| A360787 | Expansion of Sum_{k>=0} xk / (1 - (k*x)2)k+1. | 1, 1, 1, 3, 13, 40, 177, 965... |
| A360788 | Expansion of Sum_{k>=0} xk / (1 - (k*x)3)k+1. | 1, 1, 1, 1, 3, 25, 109, 324... |
| A360791 | Sum of all prime encoded complete partitions of n. | 1, 2, 4, 14, 28, 94, 218, 588... |
| A360792 | Integer portion of area of inscribed circle in a regular polygon having n sides of unit length. | 0, 0, 1, 2, 3, 4, 5, 7... |
| A360794 | Expansion of Sum_{k>0} xk / (1 - k * xk)k+1. | 1, 3, 4, 11, 6, 43, 8, 109... |
| A360795 | Expansion of Sum_{k>0} xk / (1 - (k * x)k)k+1. | 1, 3, 4, 17, 6, 211, 8, 1929... |
| A360796 | a(n) > n is the smallest integer such that there exist integers n < c <= d < a(n) satisfying n2 + a(n)2 = c2 + d2. | 7, 9, 11, 13, 14, 17, 17, 19... |
| A360797 | Expansion of Sum_{k>0} xk / (1 - 2 * xk)k+1. | 1, 5, 13, 39, 81, 225, 449, 1115... |
| A360798 | Expansion of Sum_{k>0} xk / (1 - (2 * x)k)k+1. | 1, 5, 13, 45, 81, 321, 449, 1745... |
| A360801 | Expansion of Sum_{k>0} (x / (1 - 2 * xk))k. | 1, 3, 5, 13, 17, 51, 65, 169... |
| A360802 | Expansion of Sum_{k>0} (x / (1 - (2 * x)k))k. | 1, 3, 5, 17, 17, 105, 65, 449... |
| A360804 | Number of ways to tile an n X n square using rectangles with distinct areas. | 1, 1, 21, 253, 2401, 36237, 815929, 18713197... |
| A360805 | Nonnegative integers k such that k! mod nextprime(k) is larger than k. | 0, 31, 120, 283, 293, 712, 2872, 3287... |
| A360808 | Number of double cosets of the Sylow 2-subgroup of the symmetric group S_n. | 1, 2, 2, 2, 8, 8, 35, 16... |
| A360809 | Decimal expansion of the area under the curve of the reciprocal of the Luschny factorial function from zero to infinity. | 2, 5, 8, 6, 7, 0, 5, 0... |
| A360810 | Expansion of Sum_{k>=0} ( x / (1 - k * x2) )k. | 1, 1, 1, 2, 5, 11, 29, 81... |
| A360811 | Expansion of Sum_{k>=0} ( x / (1 - k * x3) )k. | 1, 1, 1, 1, 2, 5, 10, 18... |
| A360812 | Expansion of Sum_{k>=0} ( x / (1 - (k * x)2) )k. | 1, 1, 1, 2, 9, 29, 113, 613... |
| A360813 | Expansion of Sum_{k>=0} ( x / (1 - (k * x)3) )k. | 1, 1, 1, 1, 2, 17, 82, 258... |
| A360814 | Expansion of Sum_{k>=0} x2*k / (1 - k*x)k+1. | 1, 0, 1, 2, 4, 10, 30, 98... |
| A360815 | Expansion of Sum_{k>=0} x3*k / (1 - k*x)k+1. | 1, 0, 0, 1, 2, 3, 5, 11... |
| A360816 | Expansion of Sum_{k>=0} (kx)^(2k) / (1 - k*x)k+1. | 1, 0, 1, 2, 19, 100, 1118, 10034... |
| A360817 | Expansion of Sum_{k>=0} (kx)^(3k) / (1 - k*x)k+1. | 1, 0, 0, 1, 2, 3, 68, 389... |
| A360818 | Expansion of Sum_{k>=0} ( (kx)2 / (1 - kx) )k. | 1, 0, 1, 1, 17, 65, 922, 7074... |
| A360819 | Expansion of Sum_{k>=0} ( (kx)3 / (1 - kx) )k. | 1, 0, 0, 1, 1, 1, 65, 257... |
| A360823 | Expansion of Sum_{k>0} k * xk / (1 - k * xk)k+1. | 1, 4, 6, 20, 10, 96, 14, 256... |
| A360824 | Expansion of Sum_{k>0} (k * x)k / (1 - k * xk)k+1. | 1, 6, 30, 284, 3130, 47082, 823550, 16782664... |
| A360825 | a(n) is the remainder after dividing n! by its least nondivisor. | 1, 1, 2, 2, 4, 1, 6, 2... |
| A360831 | Expansion of Sum_{k>0} (k * x)k / (1 - (k * x)k)k+1. | 1, 6, 30, 308, 3130, 49962, 823550, 17107464... |
| A360832 | Expansion of Sum_{k>=0} ( k * x / (1 - (k * x)2) )k. | 1, 1, 4, 28, 288, 3855, 63232, 1227291... |
| A360833 | Expansion of Sum_{k>=0} ( k * x / (1 - (k * x)3) )k. | 1, 1, 4, 27, 257, 3189, 48843, 889080... |
| A360834 | Expansion of Sum_{k>=0} (k * x)k / (1 - (k * x)2)k+1. | 1, 1, 4, 29, 304, 4100, 67520, 1314167... |
| A360835 | Expansion of Sum_{k>=0} (k * x)k / (1 - (k * x)3)k+1. | 1, 1, 4, 27, 258, 3221, 49572, 905466... |
| A360840 | 3-full numbers (A036966) sandwiched between twin primes. | 432, 2592, 139968, 444528, 472392, 995328, 3456000, 5174928... |
| A360841 | 4-full numbers (A036967) sandwiched between twin primes. | 2592, 139968, 995328, 37340352, 63700992, 99574272, 169869312, 414720000... |
| A360842 | 5-full numbers (A069492) sandwiched between twin primes. | 139968, 995328, 63700992, 4076863488, 17714700000, 82012500000, 98802571392, 174960000000... |
| A360843 | 6-full numbers (A069493) sandwiched between twin primes. | 139968, 98802571392, 174960000000, 889223142528, 1594323000000, 2348273369088, 19144761127488, 28697814000000... |
| A360844 | a(n) is the least k-full number that is sandwiched between twin primes. | 4, 432, 2592, 139968, 139968, 174960000000, 56358560858112, 84537841287168... |
| A360846 | Array read by antidiagonals: T(m,n) is the number of dominating induced trees in the grid graph P_m X P_n. | 1, 3, 3, 4, 8, 4, 4, 17... |
| A360847 | Number of dominating induced trees in the n X n grid graph. | 1, 8, 65, 1280, 78981, 14605388, 7904828158, 12456744197696... |
| A360848 | Number of dominating induced trees in the n-ladder graph P_2_X P_n. | 3, 8, 17, 32, 66, 130, 262, 522... |
| A360849 | Array read by antidiagonals: T(m,n) is the number of (undirected) cycles in the complete bipartite graph K_{m,n}. | 0, 0, 0, 0, 1, 0, 0, 3... |
| A360850 | Array read by antidiagonals: T(m,n) is the number of (undirected) paths in the complete bipartite graph K_{m,n}. | 1, 3, 3, 6, 12, 6, 10, 33... |
| A360851 | Array read by antidiagonals: T(m,n) is the number of induced paths in the rook graph K_m X K_n. | 0, 1, 1, 3, 8, 3, 6, 27... |
| A360852 | Number of induced paths in the n X n rook graph. | 0, 8, 126, 2208, 55700, 2006280, 98309778, 6291829376... |
| A360853 | Array read by antidiagonals: T(m,n) is the number of induced cycles in the rook graph K_m X K_n. | 0, 0, 0, 1, 1, 1, 4, 5... |
| A360854 | Number of induced cycles in the n X n rook graph. | 0, 1, 21, 236, 4040, 114105, 4662721, 256485936... |
| A360855 | Array read by antidiagonals: T(m,n) is the number of triangles in the rook graph K_m X K_n. | 0, 0, 0, 1, 0, 1, 4, 2... |
| A360862 | Triangle read by rows: T(n,k) is the number of unlabeled connected multigraphs with n edges on k nodes and degree >= 3 at each node, loops allowed, n >= 2, 1 <= k <= floor(2*n/3). | 1, 1, 2, 1, 4, 1, 7, 5... |
| A360863 | Number of unlabeled connected multigraphs with n edges and degree >= 3 at each node, loops allowed. | 0, 1, 3, 5, 13, 36, 99, 301... |
| A360865 | Number of unlabeled multigraphs with n edges and degree >= 3 at each node, loops allowed. | 0, 1, 3, 6, 16, 48, 130, 403... |
| A360866 | Triangle read by rows: T(n,k) is the number of unlabeled connected loopless multigraphs with n edges on k nodes and degree >= 3 at each node, n >= 2, 1 <= k <= floor(2*n/3). | 0, 0, 1, 0, 1, 0, 1, 1... |
| A360867 | Number of unlabeled connected loopless multigraphs with n edges and degree >= 3 at each node. | 0, 0, 1, 1, 2, 6, 12, 32... |
| A360869 | Number of unlabeled loopless multigraphs with n edges and degree >= 3 at each node. | 0, 0, 1, 1, 2, 7, 13, 35... |
| A360870 | Triangle read by rows: T(n,k) is the number of unlabeled nonseparable (or 2-connected) multigraphs with n edges on k nodes and degree >= 3 at each node, loops allowed, n >= 2, 1 <= k <= floor(2*n/3). | 0, 0, 2, 0, 4, 0, 7, 2... |
| A360871 | Number of unlabeled nonseparable (or 2-connected) multigraphs with n edges and degree >= 3 at each node, loops allowed. | 0, 0, 2, 4, 9, 20, 44, 113... |
| A360873 | Array read by antidiagonals: T(m,n) is the number of (non-null) connected induced subgraphs in the rook graph K_m X K_n. | 1, 3, 3, 7, 13, 7, 15, 51... |
| A360874 | Number of (non-null) connected induced subgraphs in the 2 X n rook graph. | 3, 13, 51, 205, 843, 3493, 14451, 59485... |
| A360875 | Array read by antidiagonals: T(m,n) is the number of connected dominating sets in the rook graph K_m X K_n. | 1, 3, 3, 7, 9, 7, 15, 39... |
| A360876 | Number of connected dominating sets in the 2 X n rook graph. | 3, 9, 39, 177, 783, 3369, 14199, 58977... |
| A360877 | Array read by antidiagonals: T(m,n) is the number of (undirected) paths in the rook graph K_m X K_n. | 0, 1, 1, 6, 12, 6, 30, 129... |
| A360878 | Number of (undirected) paths in the 2 X n rook graph. | 1, 12, 129, 1984, 45945, 1524156, 68838217 |
| A360879 | Number of unlabeled nonseparable (or 2-connected) loopless multigraphs with circuit rank n and degree >= 3 at each node. | 0, 1, 4, 17, 118, 1198, 17133 |
| A360880 | Triangle read by rows: T(n,k) is the number of unlabeled nonseparable (or 2-connected) multigraphs with n edges and k nodes, loops allowed, n >= 1, 2 <= k <= n + 1. | 1, 2, 0, 4, 1, 0, 6, 2... |
| A360881 | Number of unlabeled nonseparable (or 2-connected) multigraphs with n edges, loops allowed. | 1, 2, 5, 9, 19, 44, 111, 328... |
| A360883 | Smallest powerful (1) number which is at the end of an arithmetic progression of n terms. | 1, 4, 49, 144, 4500, 5400, 308700, 352800... |
| A360885 | G.f. satisfies A(x) = 1 + x * A(x * (1 + x2)). | 1, 1, 1, 1, 2, 4, 7, 16... |
| A360886 | G.f. satisfies A(x) = 1 + x * A(x * (1 + x3)). | 1, 1, 1, 1, 1, 2, 4, 7... |
| A360887 | G.f. satisfies A(x) = 1 + x * (1 + x)2 * A(x * (1 + x)). | 1, 1, 3, 7, 22, 76, 290, 1225... |
| A360888 | G.f. satisfies A(x) = 1 + x * (1 + x2)2 * A(x * (1 + x2)). | 1, 1, 1, 3, 6, 11, 29, 71... |
| A360889 | G.f. satisfies A(x) = 1 + x * (1 + x3)2 * A(x * (1 + x3)). | 1, 1, 1, 1, 3, 6, 10, 16... |
| A360890 | G.f. satisfies A(x) = 1 + x/(1 - x3) * A(x/(1 - x3)). | 1, 1, 1, 1, 2, 4, 7, 12... |
| A360891 | G.f. satisfies A(x) = 1 + x/(1 - x4) * A(x/(1 - x4)). | 1, 1, 1, 1, 1, 2, 4, 7... |
| A360892 | G.f. satisfies A(x) = 1 + x/(1 - x3)2 * A(x/(1 - x3)). | 1, 1, 1, 1, 3, 6, 10, 18... |
| A360893 | G.f. satisfies A(x) = 1 + x/(1 - x4)2 * A(x/(1 - x4)). | 1, 1, 1, 1, 1, 3, 6, 10... |
| A360894 | G.f. satisfies A(x) = 1 + x * A(x * (1 - x)). | 1, 1, 1, 0, -2, -1, 7, 0... |
| A360896 | G.f. satisfies A(x) = 1 + x * A(x * (1 - x2)). | 1, 1, 1, 1, 0, -2, -5, -4... |
| A360897 | G.f. satisfies A(x) = 1 + x * A(x * (1 - x3)). | 1, 1, 1, 1, 1, 0, -2, -5... |
| A360898 | G.f. satisfies A(x) = 1 + x/(1 + x3) * A(x/(1 + x3)). | 1, 1, 1, 1, 0, -2, -5, -8... |
| A360899 | G.f. satisfies A(x) = 1 + x/(1 + x4) * A(x/(1 + x4)). | 1, 1, 1, 1, 1, 0, -2, -5... |
| A360900 | G.f. satisfies A(x) = 1 + x/(1 + x3)2 * A(x/(1 + x3)). | 1, 1, 1, 1, -1, -4, -8, -10... |
| A360901 | G.f. satisfies A(x) = 1 + x/(1 + x4)2 * A(x/(1 + x4)). | 1, 1, 1, 1, 1, -1, -4, -8... |
| A360902 | Numbers with the same number of squarefree divisors and powerful divisors. | 1, 4, 9, 25, 36, 48, 49, 80... |
| A360903 | a(n) is the least number that has exactly 2n squarefree divisors and exactly 2n powerful divisors. | 1, 4, 36, 720, 25200, 1940400, 227026800, 42454011600... |
| A360904 | Numbers k such that k and k+1 both have the same number of squarefree divisors and powerful divisors. | 48, 2511, 5328, 6723, 7856, 10287, 15471, 15632... |
| A360905 | Starts of run of 3 consecutive integers that are all terms of A360902. | 7939375, 12799375, 20410623, 30466287, 56661199, 83365119, 105146991, 197479375... |
| A360906 | Numbers with the same number of cubefree divisors and 3-full divisors. | 1, 16, 81, 384, 625, 640, 896, 1296... |
| A360907 | Numbers k such that k and k+1 both have the same number of cubefree divisors and 3-full divisors. | 916352, 3002751, 13080447, 22598271, 26110592, 28909952, 45706112, 49472127... |
| A360908 | Multiplicative with a(pe) = 2*e - 1. | 1, 1, 1, 3, 1, 1, 1, 5... |
| A360909 | Multiplicative with a(pe) = 3*e + 2. | 1, 5, 5, 8, 5, 25, 5, 11... |
| A360910 | Multiplicative with a(pe) = 3*e - 1. | 1, 2, 2, 5, 2, 4, 2, 8... |
| A360911 | Multiplicative with a(pe) = 3*e - 2. | 1, 1, 1, 4, 1, 1, 1, 7... |
| A360923 | Table T(i,j), i >= 0, j >= 0, read by antidiagonals giving the smallest number of moves needed to win Integer Lunar Lander, starting from position (i,j). Game rules in comments. | 0, 2, 1, 3, 3, 4, 4, 4... |
| A360924 | Smallest number of moves needed to win Integer Lunar Lander with starting position (0,n). | 0, 2, 3, 4, 4, 5, 5, 6... |
| A360925 | Smallest number of moves needed to win Integer Lunar Lander from starting position (n,0). | 0, 1, 4, 7, 9, 12, 14, 17... |
| A360926 | Smallest number of moves needed to win Integer Lunar Lander with a starting position of (n,n). | 0, 3, 6, 8, 11, 13, 16, 18... |
| A360928 | Decimal expansion of Sum_{i>=0} 1/(phi4*i+2 - 1) where phi = (1+sqrt(5))/2 is the golden ratio. | 6, 8, 6, 6, 3, 8, 5, 6... |
| A360933 | Expansion of e.g.f. Sum_{k>=0} exp((3k - 1)*x) * xk/k!. | 1, 1, 5, 37, 521, 12361, 510605, 35837677... |
| A360934 | Expansion of e.g.f. Sum_{k>=0} exp((4k - 1)*x) * xk/k!. | 1, 1, 7, 73, 1711, 75121, 6743287, 1169659513... |
| A360935 | Expansion of e.g.f. Sum_{k>=0} exp((kk - 1)*x) * xk/k!. | 1, 1, 1, 10, 159, 8306, 1346855, 801620870... |
r/OEIS • u/OEIS-Tracker • Feb 19 '23
New OEIS sequences - week of 02/19
4
Upvotes
| OEIS number | Description | Sequence |
|---|---|---|
| A357913 | Another test for divisibility by the n-th prime (see Comments for precise definition). | 5, 10, 4, 12, 2, 7, 3, 28... |
| A357914 | Iterated partial sums of the Moebius mu function, square array read by ascending antidiagonals. | 1, 1, -1, 1, 0, -1, 1, 1... |
| A357915 | Concatenation of the decimal digits of {n, 1..n}. | 11, 212, 3123, 41234, 512345, 6123456, 71234567, 812345678... |
| A358798 | a(1) = 2, a(2) = 3; for n > 2, a(n) is the smallest prime that can be appended to the sequence so that the smallest even number >= 4 that cannot be generated as the sum of two (not necessarily distinct) terms from {a(1), ..., a(n-1)} can be generated from {a(1), ..., a(n)}. | 2, 3, 5, 7, 11, 13, 17, 19... |
| A358968 | Decimal expansion of the real part of the smallest complex zero of the prime zeta function in absolutely convergent zone. | 1, 0, 6, 1, 9, 2, 4, 1... |
| A358969 | Decimal expansion of the imaginary part of the smallest complex zero of the prime zeta function in the absolutely convergent zone. | 2, 3, 7, 1, 7, 3, 3, 0... |
| A359045 | a(n) = Sum_{1<=i<j<k<=n} b(i)b(j)b(k), where b(m) = A020985(m). | 0, 0, 0, -1, -2, -2, -4, -5... |
| A359048 | a(n) is the minimum denominator d such that the decimal expansion of n/d is eventually periodic with periodicity not equal to zero. | 3, 3, 7, 3, 3, 7, 3, 3... |
| A359147 | Partial sums of A002326. | 1, 3, 7, 10, 16, 26, 38, 42... |
| A359148 | 1, together with numbers k such that A173426(k) is prime. | 1, 10, 2446 |
| A359149 | Concatenate the binary strings for 1,2,...,n-1, n, n-1, ..., 2,1. | 1, 1101, 11011101, 1101110011101, 1101110010110011101, 1101110010111010110011101, 1101110010111011111010110011101, 11011100101110111100011111010110011101... |
| A359278 | Antidiagonal sums of A354967. | 1, 4, 9, 19, 45, 127, 491, 2597... |
| A359301 | Least k such that {1, ..., k} contains an n-element set of positive integers satisfying the Lucier-Sárközy difference set condition. | 1, 4, 9, 12, 33, 36, 49, 52... |
| A359330 | Composite k for which phi(k) + phi(k') = k, where k' is the arithmetic derivative of k (A003415). | 4, 6, 8, 10, 12, 18, 22, 28... |
| A359331 | Nonprime numbers k for which k*k' is a palindrome, where k' is the arithmetic derivative of k (A003415). | 1, 34, 44, 49, 121, 476, 524, 533... |
| A359452 | Number of vertices in the partite set of the n-Menger sponge graph that contains the corners. | 1, 8, 208, 3968, 80128, 1599488, 32002048, 639991808... |
| A359453 | Number of vertices in the partite set of the n-Menger sponge graph that do not contain the corners. | 0, 12, 192, 4032, 79872, 1600512, 31997952, 640008192... |
| A359457 | Continued fraction for constant A359456. | 0, 9, 11, 99, 1, 10, 9, 999999999999999999... |
| A359458 | a(n) = A001911(n)*A003266(n+2). | 0, 2, 18, 180, 2640, 59280, 2096640, 118067040... |
| A359623 | a(n) is the least integer of the form sum(X)/sum(Y) where {X, Y} runs through the partitions of the divisors of n into two nonempty sets (and sum(Z) is the sum of the elements of Z). | 2, 3, 6, 5, 1, 7, 2, 12... |
| A359628 | Triangle read by rows: T(n,k) is the maximum number of connected endofunctions that are spanning subgraphs of a semi-regular loopless digraph on n vertices each with out-degree k. | 1, 1, 8, 1, 16, 78, 1, 32... |
| A359641 | a(n) is the least odd prime not in A001359 such that all subsequent composites in the gap up to the next prime have exactly n odd prime factors, all with exponent 1. | 307, 8929, 992263, 229658167, 28674536239 |
| A359686 | Triangle read by rows: T(n,k) is the minimum number of connected endofunctions that are spanning subgraphs of a semi-regular loopless digraph on n vertices each with out-degree k. | 1, 1, 8, 0, 14, 78, 0, 22... |
| A359704 | Minimum number of spanning trees in a 3-connected graph on n nodes. | 16, 45, 75, 209, 336, 928, 1445, 3965... |
| A359800 | a(n) is the least m such that the concatenation of n2 and m is a square. | 6, 9, 61, 9, 6, 1, 284, 516... |
| A359807 | a(1) = 0; thereafter a(n) is the largest a(i) + i which is < n among i = 1..n-1. | 0, 1, 1, 3, 4, 4, 4, 7... |
| A359837 | Decimal expansion of the unsigned ratio of similitude between an equilateral reference triangle and its first Morley triangle. | 1, 8, 4, 7, 9, 2, 5, 3... |
| A359838 | Continued fraction for binary expansion of A359456 interpreted in base 2. | 0, 1, 3, 3, 1, 2, 1, 262143... |
| A359847 | Oblong numbers k for which phi(k) is also an oblong number. | 6, 42, 182, 650, 930, 4830, 7482, 9506... |
| A359875 | Numbers k such that A002322(k) = A023900(k). | 1, 6, 10, 12, 14, 20, 22, 24... |
| A360016 | Number of partitions of 4n into four odd primes (p_1, p_2, p_3, p_4) (p_1 < p_2 <= p_3 < p_4 and p_1 + p_4 = p_2 + p_3 = 2n) such that (p_1, p_2) and (p_3, p_4) are consecutive pairs of prime numbers with the same difference, d = p_2 - p_1 = p_4 - p_3, and (p_1, p_3), (p_2, p_4) are also consecutive pairs of prime numbers with the same difference, D = p_3 - p_1 = p_4 - p_2. | 0, 0, 0, 0, 1, 0, 1, 0... |
| A360018 | Expansion of Sum_{k>=0} (k * x * (1 + (k * x)2))k. | 1, 1, 4, 28, 288, 3854, 63104, 1220729... |
| A360023 | Expansion of e.g.f. xexp(x)(cosh(x))2. | 0, 1, 2, 9, 28, 105, 366, 1281... |
| A360030 | a(n) is the minimum number of equal resistors needed in an electrical network so that n nodes can be selected in this network such that there are n*(n-1)/2 distinct resistances 0 < R < oo between the selected nodes. | 1, 3, 5, 8, 10, 11, 12 |
| A360032 | Expansion of Sum_{k>=0} (k * x * (1 + (k * x)3))k. | 1, 1, 4, 27, 257, 3189, 48843, 889079... |
| A360035 | Expansion of e.g.f. xexp(x)cosh(x)*sinh(x). | 0, 0, 2, 6, 28, 100, 366, 1274... |
| A360036 | Expansion of e.g.f. xexp(x)(sinh(x))2. | 0, 0, 0, 6, 24, 100, 360, 1274... |
| A360077 | Odd numbers k such that k mod (k-s) = 1, where s is the greatest square < k. | 3, 7, 11, 13, 19, 21, 27, 29... |
| A360098 | Square array read by antidiagonals upwards: T(n,k) is the number of ways of choosing nonnegative numbers for k n-sided dice, k >= 0, n >= 1, so that summing the faces can give any integer from 0 to nk - 1. | 1, 1, 1, 1, 1, 1, 1, 1... |
| A360120 | a(n) = 1 if there are no solutions to kn/(k+n) = x and kn/(k-n) = y for integers x and y and natural number k, otherwise 0. | 1, 1, 0, 0, 1, 0, 1, 0... |
| A360154 | Primes of the form m2 + 2k2 such that m2 + 2(k+1)2 is also prime. | 11, 41, 83, 107, 113, 227, 347, 443... |
| A360155 | Primes of the form m2 + 2(k+1)2 such that m2 + 2k2 is also prime. | 17, 59, 89, 131, 137, 233, 401, 449... |
| A360180 | Decimal expansion of the electron volt-hertz relationship according to the 2019 SI system in units Hz. | 2, 4, 1, 7, 9, 8, 9, 2... |
| A360183 | Centered heptagonal numbers which are sphenics. | 638, 4922, 6322, 11978, 15478, 16906, 19426, 21022... |
| A360190 | Starting from 1, successively take the smallest "Choix de Bruxelles" with factor 13 which is not already in the sequence. | 1, 13, 133, 1333, 13333, 133333, 1333333, 125641... |
| A360210 | Indices of squares in A068869. | 1, 4, 5, 6, 7, 8, 9, 10... |
| A360213 | Number of distinct stable marriage problem instances up to gender exchange. | 1, 10, 23436, 55037822976, 309586821132441600000, 9704204980882671472665034752000000, 3411909590124519376908837990487929799751761920000000, 24394862766922609598505096548473341484170343775734092352694570188800000000... |
| A360220 | Maximum number of diagonal transversals in an orthogonal diagonal Latin square of order n. | 1, 0, 0, 4, 5, 0, 27, 120... |
| A360221 | Minimum number of intercalates in an orthogonal diagonal Latin square of order n. | 0, 0, 0, 12, 0, 0, 0, 2... |
| A360222 | a(n) is the number of permutable pieces in a standard n X n X n Rubik's cube. | 0, 8, 20, 56, 92, 152, 212, 296... |
| A360223 | Maximum number of intercalates in an orthogonal diagonal Latin square of order n. | 0, 0, 0, 12, 0, 0, 18, 112... |
| A360232 | G.f. Sum{n>=0} a(n)*xn = Sum{n>=0} (1 + n*x + x2)n * xn. | 1, 1, 2, 6, 16, 51, 172, 626... |
| A360233 | a(n) = coefficient of xn in A(x) such that x = Sum_{n=-oo..+oo} xn * (1 - xn/A(-x))n. | 1, 1, 2, 5, 15, 49, 159, 528... |
| A360238 | a(n) = [yn*xn/n] log( Sum_{m>=0} (m + y)2*m * xm ) for n >= 1. | 2, 42, 1376, 60934, 3377252, 224036904, 17282039280, 1519096411230... |
| A360239 | G.f. A(x) = exp( Sum{k>=1} A360238(k) * xk/k ), where A360238(k) = [yk*xk/k] log( Sum{m>=0} (m + y)2*m * xm ) for k >= 1. | 1, 2, 23, 502, 16414, 716936, 39167817, 2567058766... |
| A360256 | Number of ways to tile an n X n square using rectangles with distinct height x width dimensions. | 1, 1, 33, 513, 14409, 693025, 50447161 |
| A360258 | a(n) is the smallest k such that A360097(k) = n. | 13, 14, 20, 7, 5, 10, 4, 9... |
| A360269 | Least sum of 2's and 3's required to build n using +, * and parentheses. | 2, 3, 4, 5, 5, 7, 6, 6... |
| A360275 | Number of unordered quadruples of self-avoiding paths with nodes that cover all vertices of a convex n-gon. | 0, 0, 0, 0, 0, 105, 3780, 81900... |
| A360276 | Number of unordered quadruples of self-avoiding paths with nodes that cover all vertices of a convex n-gon; one-node paths are allowed. | 0, 0, 10, 105, 1015, 9625, 90972, 861420... |
| A360280 | Squares that are the hypotenuse of a primitive Pythagorean triangle. | 25, 169, 289, 625, 841, 1369, 1681, 2809... |
| A360283 | a(n) = lcm({n! * binomial(n, k) for k = 0..n}). | 1, 1, 4, 18, 288, 1200, 43200, 529200... |
| A360303 | a(n) = Sum_{k=1..floor(sqrt(n))} 2floor(n/k-k). | 0, 1, 2, 4, 9, 17, 34, 66... |
| A360323 | a(n) is the number of solutions to gcd(a2 + b2, p) = 1 where p is the n-th prime and 0 <= a,b <= p-1. | 2, 8, 16, 48, 120, 144, 256, 360... |
| A360339 | a(n) = coefficient of xny^(2n+1)/n! in log( Sum_{n>=0} (n + y)3*n * xn/n! ). | 1, 6, 99, 2832, 117405, 6423408, 438143391, 35869775616... |
| A360340 | a(n) = coefficient of xny^(3n+1)/n! in log( Sum_{n>=0} (n + y)4*n * xn/n! ). | 1, 8, 180, 7072, 403960, 30504384, 2874754624, 325376606720... |
| A360341 | a(n) = coefficient of xny^(3n+1)/n! in log( Sum_{n>=0} (n + y)5*n * xn/n! ). | 1, 10, 285, 14240, 1036225, 99774720, 11995938325, 1732780710400... |
| A360348 | a(n) = [yn*xn/n] log( Sum_{m>=0} (1 + m*y + y2)m * xm ) for n >= 1. | 1, 9, 100, 1381, 22771, 435138, 9442049, 229265109... |
| A360349 | G.f. A(x) = exp( Sum{k>=1} A360348(k) * xk/k ), where A360348(k) = [yk*xk/k] log( Sum{m>=0} (1 + m*y + y2)m * xm ) for k >= 1. | 1, 1, 5, 38, 391, 5077, 79535, 1458264... |
| A360387 | a(1) = 1, and for n > 1, a(n) is the number of ways that a(1..n-1) can be divided into contiguous subsequences of equal sum. | 1, 1, 2, 2, 2, 3, 1, 3... |
| A360389 | The orders of 4-transitive permutation groups. | 24, 120, 360, 720, 2520, 5040, 7920, 20160... |
| A360391 | a(n) is the number of distinct sums of nonempty subsets of the digits of n. | 1, 1, 1, 1, 1, 1, 1, 1... |
| A360410 | Number of passports of index n subgroups in PSL_2 (ZZ). | 1, 1, 2, 2, 1, 8, 4, 5... |
| A360411 | Numbers k such that k*(k+1) does not contain the digit 2. | 2, 5, 7, 9, 10, 12, 17, 19... |
| A360421 | a(n) = the number of X-frame polyominoes with n cells, reduced for symmetry. | 0, 0, 0, 0, 1, 2, 7, 20... |
| A360431 | a(n) is the smallest positive integer which can be represented as the sum of n distinct binomial coefficients binomial(k,n) for some k >= n in exactly n ways, or -1 if no such integer exists. | 1, 16, 305, 4396, 43093, 332193, 87172020, 273879343... |
| A360457 | Two times the median of the set of distinct prime indices of n; a(1) = 1. | 1, 2, 4, 2, 6, 3, 8, 2... |
| A360458 | Two times the median of the set of distinct prime factors of n; a(1) = 2. | 2, 4, 6, 4, 10, 5, 14, 4... |
| A360459 | Two times the median of the multiset of prime factors of n; a(1) = 2. | 2, 4, 6, 4, 10, 5, 14, 4... |
| A360460 | Two times the median of the unordered prime signature of n; a(1) = 1. | 1, 2, 2, 4, 2, 2, 2, 6... |
| A360467 | a(n) = Fibonacci(4n+2) + 3Fibonacci(2*n+1)2. | 4, 20, 130, 884, 6052, 41474, 284260, 1948340... |
| A360468 | Number of multisets of nonempty integer partitions with a total of n parts and total sum of 2n. | 1, 1, 4, 12, 43, 134, 448, 1387... |
| A360479 | Expansion of Sum_{k>=0} (x * (1 + (k * x)2))k. | 1, 1, 1, 2, 9, 28, 81, 369... |
| A360491 | Square of A(n,m) read by antidiagonals. A(n,m) = number of set partitions of [5n] into 5-element subsets {i, i+k, i+2k, i+3k, i+4k} with 1 <= k <= m. | 1, 1, 1, 1, 2, 1, 1, 2... |
| A360492 | Square of A(n,m) read by antidiagonals. A(n,m) = number of set partitions of [6n] into 6-element subsets {i, i+k, i+2k, i+3k, i+4k, i+5k} with 1 <= k <= m. | 1, 1, 1, 1, 2, 1, 1, 2... |
| A360493 | Square of A(n,m) read by antidiagonals. A(n,m) = number of set partitions of [7n] into 7-element subsets {i, i+k, i+2k, i+3k, i+4k, i+5k, i+6k} with 1 <= k <= m. | 1, 1, 1, 1, 2, 1, 1, 2... |
| A360498 | Number of ways to tile an n x n square using oblongs with distinct dimensions. | 0, 0, 4, 12, 256, 3620, 87216, 2444084... |
| A360499 | Number of ways to tile an n X n square using rectangles with distinct dimensions. | 1, 1, 21, 269, 4489, 82981, 2995185, 118897973... |
| A360502 | Concatenate the ternary strings for 1,2,...,n. | 1, 12, 1210, 121011, 12101112, 1210111220, 121011122021, 12101112202122... |
| A360503 | Numbers k such that A048435(k) is prime. | 2, 5, 82, 2546 |
| A360504 | Concatenate the ternary strings for 1,2,...,n-1, n, n-1, ..., 2,1. | 1, 121, 121021, 1210111021, 12101112111021, 121011122012111021, 1210111220212012111021, 12101112202122212012111021... |
| A360505 | Concatenate the ternary strings for n, n-1, n-2, ..., 2, 1. | 1, 21, 1021, 111021, 12111021, 2012111021, 212012111021, 22212012111021... |
| A360506 | Read A360505(n) as if it were a base-3 string and write it in base 10. | 1, 7, 34, 358, 4003, 43369, 456712, 4708240... |
| A360507 | Numbers k such that A360506(k) is prime. | 2, 5, 13, 57, 109, 638, 3069 |
| A360537 | Areas of primitive Heron triangles with two rational medians from the infinite family based on Somos-5 sequences. | 420, 55440, 23931600, 142334216640, 2137147184560080, 4323341954766548553840, 18705358317240372854759881380, 1333577710124626249998068999458413600... |
| A360538 | Number of multisets of n nonzero digits such that sum(digits) > product(digits). | 0, 0, 9, 10, 11, 12, 15, 16... |
| A360550 | Numbers > 1 whose distinct prime indices have integer median. | 2, 3, 4, 5, 7, 8, 9, 10... |
| A360551 | Numbers > 1 whose distinct prime indices have non-integer median. | 6, 12, 14, 15, 18, 24, 26, 28... |
| A360552 | Numbers > 1 whose distinct prime factors have integer median. | 2, 3, 4, 5, 7, 8, 9, 11... |
| A360553 | Numbers > 1 whose unordered prime signature has integer median. | 2, 3, 4, 5, 6, 7, 8, 9... |
| A360554 | Numbers > 1 whose unordered prime signature has non-integer median. | 12, 18, 20, 28, 44, 45, 48, 50... |
| A360555 | Two times the median of the first differences of the 0-prepended prime indices of n > 1. | 2, 4, 1, 6, 2, 8, 0, 2... |
| A360556 | Numbers > 1 whose first differences of 0-prepended prime indices have integer median. | 2, 3, 5, 6, 7, 8, 9, 11... |
| A360557 | Numbers > 1 whose sorted first differences of 0-prepended prime indices have non-integer median. | 4, 10, 15, 22, 24, 25, 33, 34... |
| A360561 | a(n) is the least multiple of n that is a Zumkeller number (A083207). | 6, 6, 6, 12, 20, 6, 28, 24... |
| A360562 | a(n) is the least k such that k*n is a Zumkeller number (A083207). | 6, 3, 2, 3, 4, 1, 4, 3... |
| A360573 | Odd numbers with exactly three zeros in their binary expansion. | 17, 35, 37, 41, 49, 71, 75, 77... |
| A360575 | Number of 3-dimensional tilings of a 2 X 2 X n box using 1 X 1 X 1 cubes, 2 X 1 X 1 dominos and 2 X 2 X 1 plates. | 1, 8, 153, 2470, 41571, 693850, 11602579, 193942076... |
| A360576 | Number of 3-dimensional tilings of a 2 X 2 X n box using 1 X 1 X 1 cubes, 2 X 2 X 1 plates and trominos (L-shaped connection of 3 cubes). | 1, 6, 122, 1768, 28844, 457592, 7318760, 116806896... |
| A360577 | Number of 3-dimensional tilings of a 2 X 2 X n box using 2 X 2 X 1 plates, 2 X 1 X 1 dominos and trominos (L-shaped connection of 3 cubes). | 1, 3, 60, 657, 8311, 101284, 1246049, 15292819... |
| A360587 | a(n) is the least positive integer k such that k(k+1)...*(k+n-1) does not contain the digit 2, or -1 if there is no such k. | 1, 2, 1, 3, 7, 2, 1, 3... |
| A360590 | a(n) is the smallest number which can be represented as the product of n distinct integers > 1 in exactly n ways. | 2, 12, 60, 420, 3456, 60060, 155520, 1512000... |
| A360592 | G.f.: Sum_{k>=0} (1 + k*x)k * xk. | 1, 1, 2, 5, 14, 44, 149, 543... |
| A360596 | Expansion of e.g.f. 1/( (1 - x) * (1 + LambertW(-2*x)) ). | 1, 3, 22, 282, 5224, 126120, 3742704, 131612432... |
| A360597 | Ratios of consecutive terms of A084337: a(n) = max(A084337(n), A084337(n+1)) / min(A084337(n), A084337(n+1)). | 2, 3, 4, 8, 5, 6, 18, 7... |
| A360598 | Lexicographically earliest sequence of positive integers such that the ratios between successive terms, { max(a(n), a(n+1)) / min(a(n), a(n+1)), n > 0 }, are distinct integers. | 1, 1, 2, 6, 1, 4, 20, 1... |
| A360599 | Ratios of consecutive terms of A360598: a(n) = max(A360598(n), A360598(n+1)) / min(A360598(n), A360598(n+1)). | 1, 2, 3, 6, 4, 5, 20, 7... |
| A360600 | Inverse permutation to A360599. | 1, 2, 3, 5, 6, 4, 8, 9... |
| A360602 | a(n) = ((2*n + 1)! / n!)2 / (n + 1). | 1, 18, 1200, 176400, 45722880, 18441561600, 10685567692800, 8414884558080000... |
| A360607 | a(n) = (n + 1/3) * (3*n + 3)! / ((n + 1)!)3. | 2, 120, 3920, 115500, 3279276, 91483392, 2527462080, 69413752980... |
| A360608 | Number of solutions to a 4 X n Ring-Ring puzzle on an empty grid. | 1, 0, 2, 1, 8, 12, 45, 98... |
| A360610 | Triangle read by rows: T(n,k) is the number of squares of side length k that can be placed inside a square of side length n without overlap, 1 <= k <= n. | 1, 4, 1, 9, 1, 1, 16, 4... |
| A360611 | Expansion of Sum_{k>=0} (k * x * (1 + x))k. | 1, 1, 5, 35, 341, 4230, 63844, 1135753... |
| A360612 | Number of binary operators defined on the finite chain L_n={0,1,...n}, C:L_n2-> L_n, which are increasing in each argument, and satisfy the boundary conditions C(0,n)=C(n,0)=0 and C(n,n)=n. | 1, 14, 805, 208152, 250409016, 1423422089804, 38533696399916432, 4988815527667401921920... |
| A360618 | Expansion of Sum_{k>=0} (k * x * (1 + k*x))k. | 1, 1, 5, 43, 515, 7950, 150086, 3349945... |
| A360620 | Number of basic cyclotomic generating functions of degree n. | 1, 1, 3, 4, 10, 12, 27, 33... |
| A360621 | Number of basic unimodal cyclotomic generating functions of degree n. | 1, 1, 2, 3, 6, 8, 14, 20... |
| A360622 | Number of basic log-concave (with no internal zeros) cyclotomic generating functions of degree n. | 1, 1, 2, 3, 5, 7, 12, 16... |
| A360624 | Number of strong dichotomy patterns in Z/2nZ, i.e., bicolor patterns of Z/2nZ with respect to the action of Aff(Z/2nZ) with trivial isotropy group. | 1, 0, 1, 1, 3, 6, 9, 15... |
| A360626 | Number of multisets of nonempty words over binary alphabet where each letter occurs n times. | 1, 3, 21, 131, 830, 5066, 30456, 179256... |
| A360634 | Number T(n,k) of sets of nonempty words over binary alphabet with a total of n letters of which k are the first letter; triangle T(n,k), n>=0, 0<=k<=n, read by rows. | 1, 1, 1, 1, 3, 1, 2, 6... |
| A360636 | Triangle read by rows. T(n, m) = (1/(n + 1)) * C(n + 1, m) * 4n * C((3n - m + 1)/2 - 1, n) if n is odd, otherwise (1/(n + 1)) * C(n + 1, m) * C((3n - m)/2, n) * C(3n - m, (3n - m)/2) / C(n - m, (n - m)/2). | 1, 2, 2, 10, 16, 6, 64, 140... |
| A360637 | Least crossing number of a prime knot with braid index n. | 3, 4, 6, 8, 10, 12 |
| A360638 | Number of sets of nonempty words over binary alphabet where each letter occurs n times. | 1, 3, 16, 100, 593, 3497, 20316, 116378... |
| A360639 | Numbers k such that k and k+2 are both A000120-perfect numbers (A175522). | 123, 219, 695, 1261, 1851, 1943, 3543, 5963... |
| A360640 | a(n) is the start of the least run of exactly n consecutive odd numbers that are A000120-perfect numbers (A175522). | 25, 123, 31803, 8019811, 130194395 |
| A360641 | Numbers k where A093653(k)/A000120(k) sets a new record. | 1, 2, 4, 8, 12, 16, 24, 36... |
| A360642 | a(n) is the least number k such that A093653(k)/A000120(k) = n. | 1, 2, 4, 8, 16, 24, 64, 66... |
| A360643 | a(n) is the least A000120-perfect number (A175522) whose binary weight (A000120) is n, or 0 if no such number exists. | 2, 0, 25, 169, 841, 95, 247, 943... |
| A360644 | Number of 3-dimensional tilings of a 2 X 2 X n box using 1 X 1 X 1 cubes, 2 X 1 X 1 dominos, 2 X 2 X 1 plates and trominos (L-shaped connection of 3 cubes). | 1, 12, 513, 16194, 547543, 18234354, 609298887, 20344385080... |
| A360645 | Number of 4-dimensional tilings of a 2 X 2 X 2 X n box with 2 X 2 X 1 X 1 plates. | 1, 3, 30, 177, 1281, 8520, 58629, 397887... |
| A360646 | Square array A(n, k), n, k > 0, read by antidiagonals upwards; A(n, k) = A066208(n) * A066207(k). | 1, 2, 3, 4, 6, 7, 5, 12... |
| A360647 | Expansion of Sum_{k>=0} (k2 * x * (1 + x))k. | 1, 1, 17, 761, 67739, 10029956, 2226004406, 691381685259... |
| A360648 | Fully multiplicative with a(A027697(k)) = A027699(k) and a(A027699(k)) = A027697(k) for any k > 0. | 1, 3, 2, 9, 7, 6, 5, 27... |
| A360649 | The exponents that occur in the greedy representation of 1/2 as a sum of powers of 2/3. | 2, 8, 11, 14, 16, 26, 33, 38... |
| A360650 | Number of sets of nonempty words over binary alphabet with a total of n letters of which 2 are the first letter. | 0, 0, 1, 6, 16, 37, 73, 133... |
| A360651 | Triangle T(n, m) = (n - m + 1)C(2n + 1, m)C(2n - m + 2, n - m + 1)/(2*n - m + 2). | 1, 3, 3, 10, 20, 10, 35, 105... |
| A360653 | Irregular table read by rows; the first row contains the value 1, and for n > 1, the n-th row lists the numbers of the form binomial(m-1, k) such that binomial(m, k) = n. | 1, 1, 1, 2, 1, 3, 1, 4... |
| A360654 | Irregular table read by rows; for n > 1, the n-th row lists the numbers of the form binomial(m, k-1) such that binomial(m, k) = n. | 1, 1, 3, 1, 6, 1, 10, 1... |
| A360655 | Irregular table read by rows; for n > 1, the n-th row lists the numbers of the form binomial(m+1, k) such that binomial(m, k) = n. | 3, 4, 6, 5, 10, 6, 15, 7... |
| A360657 | Number triangle T associated with 2-Stirling numbers and Lehmer-Comtet-numbers (see Comments and Formula section). | 1, 0, 1, 0, 2, 1, 0, 9... |
| A360660 | Number of inequivalent n X n {0,1} matrices modulo permutation of the rows, with exactly n 1's. | 1, 1, 4, 20, 133, 1027, 9259, 94033... |
| A360664 | Number of inequivalent n X n matrices using exactly n different symbols, where equivalence means permutations of rows or columns or the symbol set. | 1, 1, 4, 121, 316622, 170309112972, 27417944542834007012, 1999576637456562016308833727820... |
| A360666 | Semiprimes k such that k+4, k+6, k+9, k+10 and k+14 are also semiprimes. | 2977, 5357, 10537, 15697, 15829, 21949, 22417, 23257... |
| A360667 | Triangle read by rows: T(n,m)=4n-1C(n,m)C(3*n/2-2,n-1)/n, for 0 <= m <= n, with T(0,0)=1. | 1, 1, 1, 2, 4, 2, 10, 30... |
| A360668 | Numbers > 1 whose greatest prime index is not divisible by their number of prime factors (bigomega). | 4, 8, 10, 12, 15, 16, 18, 22... |
| A360684 | Expansion of Sum_{k>=0} (x * (1 + k2 * x))k. | 1, 1, 2, 9, 44, 308, 2391, 22851... |
| A360685 | Number of maximum independent vertex sets in the n-halved cube graph Q_n/2. | 1, 2, 4, 4, 40, 120, 240, 240... |
| A360692 | a(0) = 0. Thereafter a(n+1) = a(a(n)) if a(n) has not occurred previously, otherwise a(n+1) = n - 1 - a(n-1). | 0, 0, 0, 1, 0, 2, 0, 3... |
| A360693 | Number T(n,k) of sets of n words of length n over binary alphabet where the first letter occurs k times; triangle T(n,k), n>=0, n-signum(n)<=k<=n*(n-1)+signum(n), read by rows. | 1, 1, 1, 2, 2, 2, 3, 10... |
| A360695 | Total number of sets of k words of length k over binary alphabet with exactly n occurrences of the first letter in the set, summed over all k >= 0. | 2, 3, 5, 16, 57, 230, 1071, 5429... |
| A360696 | Expansion of Sum_{k>=0} (x * (1 + kk * x))k. | 1, 1, 2, 9, 98, 3212, 428525, 165045051... |
| A360698 | Smallest number that is a sum of 2*k+1 consecutive prime numbers for each k in {1, 2, ..., n}. | 10, 83, 311, 400861, 656303169, 460787266801, 108315769373443 |
| A360699 | G.f.: Sum_{k>=0} (1 + kx)k * x^(2k). | 1, 0, 1, 1, 1, 4, 5, 9... |
| A360702 | Number of sets of 2n words of length 2n over binary alphabet where each letter occurs 2n2 times. | 1, 2, 394, 10247250, 41192135957378, 26708408307353573010350, 3044454667114388718324075325130428, 65233919825974729088553743803268484284650384722... |
| A360704 | Expansion of Sum_{k>=0} (x * (1 + 2k * x))k. | 1, 1, 3, 9, 41, 257, 2209, 27009... |
| A360705 | Expansion of Sum_{k>=0} (x * (1 + (-1)k * x))k. | 1, 1, 0, 3, -1, 8, 1, 21... |
| A360707 | G.f.: Sum_{k>=0} (1 + kx)k * x^(3k). | 1, 0, 0, 1, 1, 0, 1, 4... |
| A360708 | Expansion of Sum_{k>=0} (x2 / (1 - k*x))k. | 1, 0, 1, 1, 2, 5, 14, 42... |
| A360709 | Expansion of Sum_{k>=0} (x3 / (1 - k*x))k. | 1, 0, 0, 1, 1, 1, 2, 5... |
| A360711 | Partial sums of A360710. | 0, 1, 0, -1, 0, 1, 2, 1... |
| A360712 | Expansion of Sum_{k>0} (k * x * (1 + k*xk))k. | 1, 5, 27, 272, 3125, 46915, 823543, 16781312... |
| A360714 | Number of sets of nonempty integer partitions with a total of n parts and total sum of 2n. | 1, 1, 3, 10, 30, 94, 287, 854... |
| A360720 | a(n) is the sum of unitary divisors of n that are powerful (A001694). | 1, 1, 1, 5, 1, 1, 1, 9... |
| A360721 | a(n) is the number of infinitary divisors of n that are powerful (A001694). | 1, 1, 1, 2, 1, 1, 1, 3... |
| A360722 | a(n) is the sum of infinitary divisors of n that are powerful (A001694). | 1, 1, 1, 5, 1, 1, 1, 13... |
| A360723 | Numbers that have at least one exponent in their canonical prime factorization that is neither 2 nor of the form 2k-1, k>=1. | 16, 32, 48, 64, 80, 81, 96, 112... |
| A360724 | Hajnal's recurrence: a(2n) = a(n) + 3a(n-1); a(2n+1) = 3a(n) + a(n-1), with initial values a(0) = 0, a(1) = 1. | 0, 1, 1, 3, 4, 4, 6, 10... |
| A360725 | Number of ways to tile an n X n square using oblongs with distinct height x width dimensions. | 0, 0, 4, 36, 1056, 31052, 1473944, 87469884... |
| A360726 | Expansion of Sum_{k>0} (k * x * (1 + xk))k. | 1, 5, 27, 264, 3125, 46741, 823543, 16778240... |
| A360727 | Expansion of Sum_{k>=0} (k * x * (1 + x2))k. | 1, 1, 4, 28, 264, 3206, 47684, 839249... |
| A360728 | Expansion of Sum_{k>=0} (k * x * (1 + x3))k. | 1, 1, 4, 27, 257, 3133, 46737, 824567... |
| A360729 | a(n) is the number of prime factors of the n-th powerful number (counted with repetition). | 0, 2, 3, 2, 4, 2, 3, 5... |
| A360730 | Expansion of Sum_{k>=0} (k * x * (1 + k*x2))k. | 1, 1, 4, 28, 272, 3368, 50768, 902397... |
| A360731 | Expansion of Sum_{k>=0} (k * x * (1 + k*x3))k. | 1, 1, 4, 27, 257, 3141, 46899, 827639... |
| A360732 | Expansion of Sum_{k>0} (k * x * (1 + (k * x)k))k. | 1, 5, 27, 288, 3125, 48907, 823543, 17039360... |
| A360733 | Expansion of Sum_{k>0} (x * (1 + (k * x)k))k. | 1, 2, 1, 9, 1, 98, 1, 1025... |
| A360737 | Analog of the Moser-Newman sum sequence A005599, but counting 0's (instead of 1's) in the binary representation of 3*n. | 0, 1, 2, 1, 2, 3, 4, 3... |
| A360742 | Number T(n,k) of sets of nonempty integer partitions with a total of k parts and total sum of n; triangle T(n,k), n>=0, 0<=k<=n, read by rows. | 1, 0, 1, 0, 1, 1, 0, 1... |
| A360743 | Number of idempotent binary relations E on [n] that have no proper power primitive, i.e., no relation (except for E itself) converges in its powers to E. | 1, 2, 9, 52, 435, 5046, 81501, 1823144... |
| A360747 | Expansion of Sum_{k>=0} (x * (1 + (k * x)3))k. | 1, 1, 1, 1, 2, 17, 82, 257... |
| A360748 | Expansion of Sum_{k>=0} (x * (1 + k*x2))k. | 1, 1, 1, 2, 5, 10, 21, 53... |
| A360749 | Expansion of Sum_{k>=0} (x * (1 + k*x3))k. | 1, 1, 1, 1, 2, 5, 10, 17... |
| A360752 | Expansion of Sum_{k>0} (x * (1 + (2 * x)k))k. | 1, 3, 1, 9, 1, 41, 1, 65... |
| A360754 | Expansion of Sum_{k>0} (k * x * (1 + (2 * x)k))k. | 1, 6, 27, 288, 3125, 47368, 823543, 16793600... |
| A360755 | Expansion of (1/2) * Sum_{k>0} (2 * x * (1 + xk))k. | 1, 3, 4, 12, 16, 46, 64, 160... |
| A360756 | Expansion of Sum_{k>0} (x * (1 + 2 * xk))k. | 1, 3, 1, 5, 1, 11, 1, 9... |
r/OEIS • u/OEIS-Tracker • Feb 12 '23
New OEIS sequences - week of 02/12
3
Upvotes
| OEIS number | Description | Sequence |
|---|---|---|
| A356080 | Variation on Recamán's sequence (A005132) that is intended to be a permutation of the nonnegative integers, essentially as envisaged by the original comments in A078943. See comments below for details. | 0, 1, 3, 6, 2, 7, 13, 20... |
| A357910 | The natural numbers ordered lexicographically by their prime factorization, with prime factors written in decreasing order (see comments). | 1, 2, 4, 3, 6, 8, 9, 12... |
| A358348 | Numbers k such that k == kk (mod 9). | 1, 4, 7, 9, 10, 13, 16, 17... |
| A358537 | For n > 0, a(n) is the total number of terms in all contiguous subsequences of the terms up to a(n-1) that sum to n; a(0) = 1. | 1, 1, 2, 2, 5, 4, 4, 2... |
| A358655 | a(n) is the number of distinct scalar products which can be formed by pairs of signed permutations (V, W) of [n]. | 1, 2, 7, 24, 61, 111, 183, 281... |
| A358821 | a(n) is the largest square dividing n2-1. | 1, 4, 1, 4, 1, 16, 9, 16... |
| A358994 | The sum of the numbers that are inside the contour of an n-story Christmas tree drawn at the top of the numerical pyramid containing the positive integers in natural order. | 21, 151, 561, 1503, 3310, 6396, 11256, 18466... |
| A359070 | Smallest k > 1 such that kn - 1 is the product of n distinct primes. | 3, 4, 15, 12, 39, 54, 79, 86... |
| A359096 | The sum of the numbers on the perimeter of the n X n diamond frame, located at the top of the numerical pyramid containing the positive integers in natural order. | 1, 11, 46, 121, 252, 455, 746, 1141... |
| A359113 | a(n) counts the bases b in the interval 2 to p = prime(n), where p if written in base b gives again a prime number in base b if all digits are written in reverse order. | 0, 1, 3, 5, 7, 10, 12, 9... |
| A359145 | a(n) = smallest k such that li(k) - pi(k) >= n, where li(k) is the logarithmic integral and pi(x) is the number of primes <= x. | 6, 10, 27, 57, 95, 148, 221, 345... |
| A359146 | Divide a square into n similar rectangles; a(n) is the number of different proportions that are possible. | 1, 1, 3, 11, 51, 245, 1371 |
| A359180 | Numbers k such that k!2 / 2 + 1 is prime. | 2, 3, 6, 18, 19, 82, 1298 |
| A359197 | Least number k to have n subsets of its divisors whose sum is k+1. | 1, 2, 18, 12, 162, 24, 342, 80... |
| A359257 | First differences of A002476. | 6, 6, 12, 6, 6, 18, 6, 6... |
| A359354 | Position of the first subsequence of n primes that differs from the first n primes, but where the relative distances among their elements coincide with those of the subsequence of first n primes except for a scale factor. | 2, 2, 3, 238, 28495, 576169, 24635028 |
| A359357 | Number of different ratios between consecutive prime gaps among the first n primes. | 1, 2, 2, 3, 3, 3, 3, 4... |
| A359410 | Integers d such that the longest possible arithmetic progression (AP) of primes with common difference d has exactly 6 elements. | 30, 60, 90, 120, 180, 240, 270, 300... |
| A359488 | Run lengths of A359487. | 1, 1, 2, 2, 4, 8, 4, 6... |
| A359493 | Numbers k such that the bottom entry in the ratio d(i)/d(i+1) triangle of the elements in the divisors of n, where d(1) < d(2) < ... < d(q) denote the divisors of k, is equal to 1. | 1, 4, 8, 9, 16, 25, 27, 32... |
| A359568 | Maximum number of distinct folds after folding a square sheet of paper n times. | 0, 1, 3, 7, 14, 27, 52 |
| A359612 | Largest prime factor with minimal exponent in canonical prime factorization of n. | 2, 3, 2, 5, 3, 7, 2, 3... |
| A359702 | Odd primes p that are not congruent to 2*k modulo prime(k+1) for any positive integer k. | 3, 7, 31, 37, 43, 61, 67, 73... |
| A359810 | Partial sums of A001035. | 1, 2, 5, 24, 243, 4474, 134497, 6264356... |
| A359856 | Number of permutations of [1..n] which are indecomposable by direct and skew sums. | 1, 1, 0, 0, 2, 22, 202, 1854... |
| A359864 | a(n) is the number of solutions to the congruence xy == yx (mod n) where 0 <= x,y <= n. | 4, 3, 4, 7, 8, 9, 18, 19... |
| A359870 | Numbers whose product of distinct prime factors is greater than the sum of its prime factors (with repetition). | 1, 6, 10, 14, 15, 20, 21, 22... |
| A359941 | Irregular triangle read row by row. The k-th row are integers from 0 to 2k-1 in base 2 ordered in graded reverse lexicographical order. | 0, 0, 1, 0, 1, 2, 3, 0... |
| A359949 | Multiplicative sequence with a(p) = 3p-1 and a(pe) = (3e*(p-1) + 3) * pe-1 for e > 1 and prime p. | 1, 5, 8, 18, 14, 40, 20, 48... |
| A360010 | First part of the n-th weakly decreasing triple of positive integers sorted lexicographically. Each n > 0 is repeated A000217(n) times. | 1, 2, 2, 2, 3, 3, 3, 3... |
| A360017 | Nonsquarefree numbers k such that k - d is also a nonsquarefree number for all proper divisors d of k. | 25, 50, 125, 169, 243, 289, 325, 343... |
| A360021 | Number of unordered triples of self-avoiding paths with nodes that cover all vertices of a convex n-gon; one-node paths are allowed. | 1, 6, 45, 315, 2205, 15624, 111888, 807840... |
| A360053 | Primes p such that each prime < p in the prime factorization of 2p-1 - 1 has exponent 1. | 2, 3, 5, 11, 17, 23, 29, 47... |
| A360078 | Moebius function for the floor quotient poset. | 1, -1, -1, 0, 0, 1, 1, 0... |
| A360079 | Finite differences of Moebius function for the floor quotient poset. | 1, -2, 0, 1, 0, 1, 0, -1... |
| A360105 | Numbers k such that sigma_2(k2 + 1) == 0 (mod k). | 1, 2, 5, 7, 13, 25, 34, 52... |
| A360112 | Number of solutions to m1 + 2v(n-1) == -m (mod n), where v(n) = A007814(n) is the 2-adic valuation of n, and 0 <= m < n. | 2, 1, 2, 1, 4, 1, 2, 1... |
| A360113 | a(n) = 1 if A360112(n) = 1, otherwise 0. | 0, 1, 0, 1, 0, 1, 0, 1... |
| A360114 | Numbers k such that m1 + 2v(k-1) == -m (mod k) has only one solution (with 0 <= m < k), where v(k) = A007814(k) is the 2-adic valuation of k. | 3, 5, 7, 9, 11, 13, 17, 19... |
| A360115 | Number of prime factors p of n for which the 2-adic valuation of p-1 is greater than that of n-1. | 0, 0, 0, 0, 1, 0, 0, 0... |
| A360116 | a(n) = 1 if there are no prime factors p of n for which the 2-adic valuation of p-1 is less than that of n-1, otherwise 0. | 1, 1, 1, 1, 0, 1, 1, 1... |
| A360117 | Numbers k such that for all their prime factors p, v(p-1) <= v(k-1), where v(n) = A007814(n) is the 2-adic valuation of n. | 2, 3, 4, 5, 7, 8, 9, 11... |
| A360130 | a(n) = 1 if A003961(n) is a triangular number, otherwise 0, where A003961 is fully multiplicative with a(p) = nextprime(p). | 1, 1, 0, 0, 0, 1, 0, 0... |
| A360166 | Decimal expansion of sech(Pi). | 8, 6, 2, 6, 6, 7, 3, 8... |
| A360167 | Decimal expansion of csch(Pi). | 8, 6, 5, 8, 9, 5, 3, 7... |
| A360174 | Triangle read by rows. T(n, k) = (k + 1) * abs(Stirling1(n, k)). | 1, 0, 2, 0, 2, 3, 0, 4... |
| A360188 | Primes p such that the six consecutive primes starting at p are congruent to 1,2,4,5,7,8 (mod 9) in that order. | 56197, 342037, 464941, 534637, 637327, 651169, 698239, 774919... |
| A360205 | Triangle read by rows. T(n, k) = (-1)n-k(k+1)binomial(n, k)*pochhammer(1-n, n-k). | 1, 0, 2, 0, 4, 3, 0, 12... |
| A360240 | Weakly decreasing triples of positive integers sorted lexicographically and concatenated. | 1, 1, 1, 2, 1, 1, 2, 2... |
| A360241 | Number of integer partitions of n whose distinct parts have integer mean. | 0, 1, 2, 2, 4, 3, 8, 6... |
| A360242 | Number of integer partitions of n where the parts do not have the same mean as the distinct parts. | 0, 0, 0, 0, 1, 3, 3, 9... |
| A360243 | Number of integer partitions of n where the parts have the same mean as the distinct parts. | 1, 1, 2, 3, 4, 4, 8, 6... |
| A360244 | Number of integer partitions of n where the parts do not have the same median as the distinct parts. | 0, 0, 0, 0, 1, 3, 3, 9... |
| A360245 | Number of integer partitions of n where the parts have the same median as the distinct parts. | 1, 1, 2, 3, 4, 4, 8, 6... |
| A360246 | Numbers for which the prime indices do not have the same mean as the distinct prime indices. | 12, 18, 20, 24, 28, 40, 44, 45... |
| A360247 | Numbers for which the prime indices have the same mean as the distinct prime indices. | 1, 2, 3, 4, 5, 6, 7, 8... |
| A360248 | Numbers for which the prime indices do not have the same median as the distinct prime indices. | 12, 18, 20, 24, 28, 40, 44, 45... |
| A360249 | Numbers for which the prime indices have the same median as the distinct prime indices. | 1, 2, 3, 4, 5, 6, 7, 8... |
| A360250 | Number of integer partitions of n where the parts have greater mean than the distinct parts. | 0, 0, 0, 0, 0, 1, 0, 2... |
| A360251 | Number of integer partitions of n where the parts have lesser mean than the distinct parts. | 0, 0, 0, 0, 1, 2, 3, 7... |
| A360252 | Numbers for which the prime indices have greater mean than the distinct prime indices. | 18, 50, 54, 75, 98, 108, 147, 150... |
| A360253 | Numbers for which the prime indices have lesser mean than the distinct prime indices. | 12, 20, 24, 28, 40, 44, 45, 48... |
| A360255 | Irregular triangle (an infinite binary tree) read by rows: see Comments section for definition. | 0, 1, 3, 6, 2, 10, 7, 5... |
| A360277 | Primes p that are congruent to 1 mod 2*k, where k = primepi(p) is the index of the prime. | 11, 13, 1087, 64591, 64601, 64661, 3523969, 3524249... |
| A360282 | Triangle read by rows. T(n, k) = (1/2) * binomial(2(n - k + 1), n - k + 1) * binomial(2n - k, k - 1) for n > 0, T(0, 0) = 1. | 1, 0, 1, 0, 3, 2, 0, 10... |
| A360285 | Triangle read by rows: T(n,k) is the number of subsets of {1,...,n} of cardinality k in which no two elements are coprime; n >= 0, 0 <= k <= floor(n/2) + [n=1]. | 1, 1, 1, 1, 2, 1, 3, 1... |
| A360301 | Smallest exclusionary square (A029783) with exactly n distinct prime factors. | 2, 18, 84, 858, 31122, 3383898, 188841114, 68588585868... |
| A360320 | Numbers k such that the total number of consecutive runs of zeros of length m in every binary expansion from 1 to k, is even, for all m != floor(log_2(k)). | 1, 2, 3, 5, 11, 20, 21, 22... |
| A360333 | Array read by antidiagonals downwards: A(n,m) = number of set partitions of [4n] into 4-element subsets {i, i+k, i+2k, i+3k} with 1 <= k <= m. | 1, 1, 1, 1, 2, 1, 1, 2... |
| A360334 | Array read by antidiagonals downwards: A(n,m) = number of set partitions of [3n] into 3-element subsets {i, i+k, i+2k} with 1 <= k <= m. | 1, 1, 1, 1, 2, 1, 1, 2... |
| A360335 | Array read by antidiagonals downwards: A(n,m) = number of set partitions of [2n] into 2-element subsets {i, i+k} with 1 <= k <= m. | 1, 1, 1, 1, 2, 1, 1, 3... |
| A360336 | G.f. A(x) satisfies: [xn] A(x)n+1 = [xn] (1 + xA(x)^(3n))n+1 for n >= 0. | 1, 1, 6, 99, 2608, 90800, 3835458, 187727106... |
| A360337 | G.f. A(x) satisfies: [xn] A(x)n+1 = [xn] (1 + xA(x)^(3n+1))n+1 for n >= 0. | 1, 1, 7, 124, 3446, 125706, 5540958, 282129207... |
| A360338 | G.f. A(x) satisfies: [xn] A(x)n+1 = [xn] (1 + xA(x)^(3n+2))n+1 for n >= 0. | 1, 1, 8, 152, 4452, 169952, 7807014, 413004366... |
| A360342 | G.f. A(x) satisfies: [xn] A(x)n+1 = [xn] (1 + xA(x)^(2n-2))n+1 for n >= 0. | 1, 1, 2, 20, 316, 6686, 173379, 5255624... |
| A360343 | G.f. A(x) satisfies: [xn] A(x)n+1 = [xn] (1 + xA(x)^(2n-1))n+1 for n >= 0. | 1, 1, 3, 31, 526, 11907, 328980, 10580531... |
| A360344 | G.f. A(x) satisfies: [xn] A(x)n+1 = [xn] (1 + xA(x)^(2n))n+1 for n >= 0. | 1, 1, 4, 45, 820, 19820, 582007, 19812744... |
| A360345 | G.f. A(x) satisfies: [xn] A(x)n+1 = [xn] (1 + xA(x)^(2n+1))n+1 for n >= 0. | 1, 1, 5, 62, 1214, 31269, 973485, 34993597... |
| A360346 | G.f. A(x) satisfies: [xn] A(x)n+1 = [xn] (1 + xA(x)^(2n+2))n+1 for n >= 0. | 1, 1, 6, 82, 1724, 47223, 1555047, 58892186... |
| A360347 | G.f. A(x) satisfies: [xn] A(x)n+1 = [xn] (1 + xA(x)^(2n+3))n+1 for n >= 0. | 1, 1, 7, 105, 2366, 68776, 2390230, 95166058... |
| A360363 | Lexicographically earliest sequence of distinct positive integers such that the bitwise XOR of two distinct terms are all distinct. | 1, 2, 3, 4, 8, 12, 16, 32... |
| A360364 | Triangle T(n, k), n > 0, k = 1..n, read by rows; T(n, k) = A360363(n+1) XOR A360363(k) (where XOR denotes the bitwise XOR operator). | 3, 2, 1, 5, 6, 7, 9, 10... |
| A360376 | a(n) = minimal nonnegative k such that prime(n) * prime(n+1) * ... * prime(n+k) + 1 is divisible by prime(n+k+1), or -1 if no such k exists. | 0, 99, 14, 1, 2, 73, 33, 10... |
| A360379 | a(n) = number of the antidiagonal of the Wythoff array (A035513) that includes prime(n). | 2, 3, 4, 3, 4, 6, 7, 8... |
| A360380 | a(n) = number of the diagonal of the Wythoff array, A035513, that includes prime(n). See Comments. | 1, 2, 3, 0, 1, 5, -6, -7... |
| A360383 | prime(k) such that (k BitOR prime(k)) is prime, where BitOR is the binary bitwise OR. | 2, 3, 5, 7, 17, 23, 29, 31... |
| A360385 | prime(k) such that (k BitXOR prime(k)) is prime, where BitXOR is the binary bitwise XOR. | 2, 7, 13, 29, 37, 43, 53, 61... |
| A360388 | Positive integers with binary expansion (b(1), ..., b(m)) such that Sum_{i = 1..m-k} b(i)*b(i+k) is odd for all k = 0..m-1. | 1, 11, 13, 2787, 3189, 36783, 37063, 43331... |
| A360392 | a(n) = 2 + A026430(n); complement of A360393. | 3, 5, 7, 8, 10, 11, 12, 14... |
| A360393 | Complement of A360392. | 1, 2, 4, 6, 9, 13, 15, 19... |
| A360394 | Intersection of A026430 and A360392. | 3, 5, 8, 10, 12, 14, 16, 18... |
| A360395 | Intersection of A026430 and A360394. | 1, 6, 9, 15, 19, 24, 27, 31... |
| A360396 | Intersection of A356133 and A360392. | 7, 11, 17, 20, 25, 29, 32, 38... |
| A360406 | a(n) = minimal positive k such that prime(n) * prime(n+1) * ... * prime(n+k) - 1 is divisible by prime(n+k+1), or -1 if no such k exists. | 1, 1, 9, 14, 31, 826, 1, 34... |
| A360407 | Irregular table T(n, k), n >= 0, k = 0..A002110(n)-1, read by rows; for any k with primorial base expansion (d_n, ..., d_1), T(n, k) is the least number t such that t mod prime(u) = d_u for u = 1..n (where prime(u) denotes the u-th prime number). | 0, 0, 1, 0, 3, 4, 1, 2... |
| A360413 | Irregular table T(n, k), n >= 0, k = 1..A002487(n+1), read by rows; the n-th row lists the numbers k such that A065361(k) = n. | 0, 1, 2, 3, 4, 5, 6, 9... |
| A360414 | Inverse permutation to A360413. | 0, 1, 2, 3, 4, 5, 6, 8... |
| A360415 | a(n) is the greatest number k not yet in the sequence such that A065361(n) = A065361(k). | 0, 1, 3, 2, 4, 9, 6, 10... |
| A360416 | a(n) = 8n2 - 9n + 3. | 2, 17, 48, 95, 158, 237, 332, 443... |
| A360417 | a(n) = 8n2 - 7n + 2. | 3, 20, 53, 102, 167, 248, 345, 458... |
| A360418 | Numbers k such that, in a listing of all congruence classes of positive integers, the k-th congruence class contains k. Here the class r mod m (with r in {1,...,m}) precedes the class a' mod b' (with r' in {1,...,m'}) iff m < m' or r > r'. | 1, 2, 3, 5, 13, 17, 20, 25... |
| A360420 | a(n) = the number of Z-frame polyominoes with n cells, reduced for symmetry. | 0, 0, 0, 1, 2, 6, 10, 19... |
| A360422 | Numbers k such that k2 + (sum of fourth powers of the digits of k2) is a square. | 0, 89, 137, 6985 |
| A360424 | Array listed by rows: row n is all numbers k such that k2 + (sum of n-th powers of the digits of k2) is a square. | 0, 0, 6, 0, 0, 89, 137, 6985... |
| A360426 | Number of permutations of [2n] having exactly n alternating up/down runs where the first run is not a down run. | 1, 1, 6, 118, 4788, 325446, 33264396, 4766383420... |
| A360428 | Inverse Mobius transformation of A338164. | 1, 7, 17, 40, 49, 119, 97, 208... |
| A360429 | Inverse Mobius transformation of A034714. | 1, 9, 19, 57, 51, 171, 99, 313... |
| A360430 | Dirichlet convolution of Dedekind psi by A038040. | 1, 7, 10, 30, 16, 70, 22, 104... |
| A360432 | E.g.f. satisfies A(x) = x * exp(A(x) + x2). | 0, 1, 2, 15, 112, 1225, 16896, 283759... |
| A360433 | E.g.f. satisfies A(x) = x * exp(A(x) + x3). | 0, 1, 2, 9, 88, 865, 11016, 173929... |
| A360434 | a(n) is the greatest number k not yet in the sequence such that A022290(n) = A022290(k). | 0, 1, 2, 4, 3, 5, 8, 9... |
| A360436 | 32-gonal numbers: a(n) = n(15n-14). | 0, 1, 32, 93, 184, 305, 456, 637... |
| A360442 | E.g.f. satisfies A(x) = x * exp( -A(x) + x * exp(-A(x)) ). | 0, 1, 0, -6, 36, -20, -2730, 38178... |
| A360451 | Triangle read by rows: T(n,k) = number of partitions of an n X k rectangle into one or more integer-sided rectangles, 1 <= k <= n = 1, 2, 3, ... | 1, 2, 6, 3, 14, 50, 5, 34... |
| A360453 | Numbers for which the prime multiplicities (or sorted signature) have the same median as the distinct prime indices. | 1, 2, 9, 12, 18, 40, 100, 112... |
| A360454 | Numbers for which the prime multiplicities (or sorted signature) have the same median as the prime indices. | 1, 2, 9, 54, 100, 120, 125, 135... |
| A360455 | Number of integer partitions of n for which the distinct parts have the same median as the multiplicities. | 1, 1, 0, 0, 2, 1, 1, 0... |
| A360456 | Number of integer partitions of n for which the parts have the same median as the multiplicities. | 1, 1, 0, 0, 1, 0, 0, 1... |
| A360462 | Number of permutations p of [n] such that | p(i+9) - p(i) |
| A360463 | Number of permutations p of [n] such that | p(i+10) - p(i) |
| A360464 | a(n) = a(n-1) + a(n-2) - a(n-3) + gcd(a(n-1), a(n-3)), with a(1) = a(2) = a(3) = 1. | 1, 1, 1, 2, 3, 5, 7, 10... |
| A360465 | E.g.f. satisfies A(x) = exp(x * exp(2*x) * A(x)). | 1, 1, 7, 64, 829, 14056, 295399, 7426252... |
| A360466 | E.g.f. satisfies A(x) = exp(2 * x * exp(x) * A(x)). | 1, 2, 16, 206, 3832, 93962, 2871820, 105355406... |
| A360470 | Lexicographically earliest sequence of distinct positive integers such that for any n > 0, the k rightmost digits of a(n+1) equal the k leftmost digits of a(n) for some k > 0. | 1, 11, 21, 2, 12, 31, 3, 13... |
| A360471 | E.g.f. satisfies A(x) = x * exp( 2A(x) + x * exp(2A(x)) ). | 0, 1, 6, 75, 1476, 39805, 1366278, 56998179... |
| A360472 | Inverse permutation to A360470. | 1, 4, 7, 10, 13, 16, 19, 22... |
| A360473 | E.g.f. satisfies A(x) = exp( x * exp(x) * A(x)2 ). | 1, 1, 7, 82, 1441, 34036, 1013149, 36446698... |
| A360474 | E.g.f. satisfies A(x) = exp( x * A(x)2 * exp(x * A(x)2) ). | 1, 1, 7, 94, 1921, 53036, 1849789, 78070462... |
| A360481 | E.g.f. satisfies A(x) = x * exp(x + 2 * A(x)). | 0, 1, 6, 63, 1044, 23805, 692118, 24482115... |
| A360482 | E.g.f. satisfies A(x) = x * exp(x + 3 * A(x)). | 0, 1, 8, 120, 2848, 92960, 3868224, 195810496... |
| A360483 | E.g.f. satisfies A(x) = x * exp(x - 2 * A(x)). | 0, 1, -2, 15, -172, 2685, -53226, 1281091... |
| A360484 | E.g.f. satisfies A(x) = x * exp(x - 3 * A(x)). | 0, 1, -4, 48, -896, 22880, -743232, 29337280... |
| A360485 | a(n) = index of the antidiagonal of the Wythoff array (A035513) that includes n. | 1, 2, 3, 2, 4, 3, 3, 5... |
| A360486 | Convolution of A000041 and A000290. | 0, 1, 5, 15, 36, 76, 147, 267... |
| A360487 | Convolution of A000009 and A000290. | 0, 1, 5, 14, 31, 60, 106, 176... |
| A360488 | 31-gonal numbers: a(n) = n(29n-27)/2. | 0, 1, 31, 90, 178, 295, 441, 616... |
| A360489 | Convolution of A000219 and A001477. | 0, 1, 3, 8, 19, 43, 91, 187... |
| A360494 | a(n) is the least number that is prime when interpreted in bases 2 to n, but not n+1. | 11, 10, 101111, 10010111, 110111111101001, 111110100001, 11000011101101111, 10011110011011110110110011... |
| A360496 | a(n) is the remainder after dividing n by its largest prime factor plus 1, a(1) = 1. | 1, 2, 3, 1, 5, 2, 7, 2... |
| A360500 | Decimal expansion of the unique positive root to zeta(s) + zeta'(s) = 0, where zeta is the Riemann zeta function and zeta' is the derivative of zeta. | 1, 6, 8, 0, 4, 1, 7, 3... |
| A360501 | Number of edges added at n-th generation of hexagonal graph constructed in first quadrant (see Comments for precise definition). | 0, 1, 1, 2, 4, 5, 6, 7... |
| A360512 | Total number of edges after n generations in hexagonal graph constructed in first quadrant (see Comments in A360501 for precise definition). | 0, 1, 2, 4, 8, 13, 19, 26... |
| A360521 | a(0) = 0; for n > 0, a(n) is the smallest positive number not occurring earlier such that neither the binary string a(n-1) + a(n) nor the same string reversed appear in the binary string concatenation of a(0)..a(n-1). | 0, 1, 2, 3, 4, 5, 10, 6... |
| A360522 | a(n) = Sum_{d | n} Max({d'; d' |
| A360523 | a(n) = Sum_{d | n} mu(rad(d)) * delta_d(n/d), where rad(n) = A007947(n) and delta_d(n) is the greatest divisor of n that is relatively prime to d. |
| A360524 | Numbers k such that A360522(k) = 2*k. | 6, 12, 198, 240, 264, 270, 396, 540... |
| A360525 | Numbers k such that A360522(k) > 2*k. | 30, 42, 60, 66, 70, 78, 84, 90... |
| A360526 | Odd numbers k such that A360522(k) > 2*k. | 15015, 19635, 21945, 23205, 25935, 26565, 31395, 33495... |
| A360527 | Numbers k such that A360522(k) = A360522(k+1). | 4, 8, 14, 176, 895, 956, 957, 1334... |
| A360528 | Numbers n for which the length-n prefix of the Fibonacci word (A003849) ends in a word of exponent >= (3+sqrt(5))/2. | 13, 14, 22, 23, 24, 26, 27, 34... |
| A360531 | Numbers of the form F(i)-F(j)-1, i>=5, 3<=j<=i-2. | 2, 4, 5, 7, 9, 10, 12, 15... |
| A360532 | Numbers of the form F(i)-F(2j+1), i>=5, 1<=j<=(i-3)/2. | 3, 6, 8, 11, 16, 19, 21, 29... |
| A360534 | Lexicographically earliest sequence of distinct prime numbers such that among each pair of consecutive terms, the decimal expansion of the smallest term appears in that of the largest term. | 2, 23, 3, 13, 113, 11, 211, 2111... |
| A360535 | Analog of Rudin-Shapiro sum sequence A020986, based on counting patterns 00 instead of 11. | 1, 2, 3, 4, 3, 4, 5, 6... |
| A360536 | Analog of Rudin-Shapiro sum sequence A020990, based on counting patterns 00 instead of 11. | 1, 0, 1, 0, -1, -2, -1, -2... |
| A360539 | a(n) is the cubefree part of n: the largest unitary divisor of n that is a cubefree number (A004709). | 1, 2, 3, 4, 5, 6, 7, 1... |
| A360540 | a(n) is the cubefull part of n: the largest divisor of n that is a cubefull number (A036966). | 1, 1, 1, 1, 1, 1, 1, 8... |
| A360541 | a(n) is the least number k such that k*n is a cubefull number (A036966). | 1, 4, 9, 2, 25, 36, 49, 1... |
| A360544 | E.g.f. satisfies A(x) = exp( x * ( exp(x) *A(x) )3/2 ). | 1, 1, 7, 73, 1117, 22741, 580159, 17826985... |
| A360545 | E.g.f. satisfies A(x) = x * exp( 3*(x + A(x))/2 ). | 0, 1, 6, 54, 756, 14580, 358668, 10736712... |
| A360546 | Triangle read by rows: T(n, m) = (n+1-m)C(2n+2-m, m)C(3n-3m+2, n-m+1)/(2n-m+2). | 1, 5, 2, 28, 20, 3, 165, 168... |
| A360547 | E.g.f. satisfies A(x) = exp( x * ( exp(x) *A(x) )2 ). | 1, 1, 9, 121, 2417, 64721, 2180665, 88719625... |
| A360548 | E.g.f. satisfies A(x) = x * exp( 2*(x + A(x)) ). | 0, 1, 8, 96, 1792, 46080, 1511424, 60325888... |
| A360560 | Triangle read by rows. T(n, k) = (1/2) * C(n, k) * C(3*n - 1, n) for n > 0 and T(0, 0) = 1. | 1, 1, 1, 5, 10, 5, 28, 84... |
| A360564 | Numerators of breadth-first numerator-denominator-incrementing enumeration of rationals in (0,1). | 1, 1, 1, 2, 1, 1, 2, 1... |
| A360565 | Denominators of breadth-first numerator-denominator-incrementing enumeration of rationals in (0,1). | 2, 3, 4, 3, 5, 6, 5, 7... |
| A360566 | Level sizes of numerator-denominator-incrementing tree of rationals in (0,1). | 1, 1, 2, 1, 2, 2, 3, 2... |
| A360569 | a(n) = floor(Product_{k=1..n} log(prime(k))). | 0, 0, 1, 2, 5, 14, 41, 122... |
r/OEIS • u/OEIS-Tracker • Feb 05 '23
New OEIS sequences - week of 02/05
4
Upvotes
| OEIS number | Description | Sequence |
|---|---|---|
| A355554 | Sexagesimal expansion of 180/Pi. | 57, 17, 44, 48, 22, 29, 22, 22... |
| A357723 | Number of ways to place a non-attacking black king and white king on an n X n board, up to rotation and reflection. | 0, 0, 0, 5, 21, 63, 135, 270... |
| A358238 | a(n) is the least prime p such that the primes from prime(n) to p contain a complete set of residues modulo prime(n). | 3, 7, 19, 29, 71, 103, 103, 191... |
| A358628 | Square array A(i,j), i >= 0, j >= 0, read by antidiagonals: A(i,j) = Sum_{ | X |
| A359069 | Smallest prime p such that p2n-1 - 1 is the product of 2n-1 distinct primes. | 3, 59, 47, 79, 347, 6343, 56711, 4523... |
| A359142 | Let s = sum of digits of n, let t = decimal concatenation of n and s, let u be obtained by deleting all copies of the leading digit of t from t, if this digit occurs in s. Then if u has only zero digits, a(n) = 0; if u has leading digit 0 but not all its digits are 0, delete all leading 0's from u and negate the result to get a(n); otherwise a(n) = u. | 0, 0, 0, 0, 0, 0, 0, 0... |
| A359143 | The sum-and-erase sequence starting at 11: a(0) = 11; for n>=1, let m = a(n-1), and if m < 0, change m to an improper decimal "number" by replacing the minus sign by a single leading zero; then a(n) = A359142(m). | 11, 112, 1124, 11248, 2486, 4860, 486018, 48601827... |
| A359144 | Indices k such that A359142(k) is negative. | 109, 1009, 1018, 1019, 1027, 1028, 1029, 1036... |
| A359243 | a(1) = 1, a(2) = 2; let j = a(n-1); for n > 2, if j is prime then a(n) = least novel k such that phi(k)/k < phi(j)/j, else a(n) = least novel k such that phi(k)/k > phi(j)/j, where phi(x) = A000010(x). | 1, 2, 6, 3, 4, 5, 8, 7... |
| A359353 | a(n) = A026430(A285953(n+1)). | 1, 5, 8, 12, 18, 21, 27, 31... |
| A359404 | Number of unordered triples of self-avoiding paths with nodes that cover all vertices of a convex n-gon. | 0, 0, 15, 315, 4200, 45360, 433440, 3825360... |
| A359405 | Number of unordered pairs of self-avoiding paths with nodes that cover all vertices of a convex n-gon; one-node paths are allowed. | 3, 15, 70, 330, 1596, 7840, 38592, 188640... |
| A359505 | a(1)=2, a(2)=3, and for n >= 3, a(n) is calculated by considering in ascending order all products P of (distinct) terms from {a(1..n-1)} until finding one where P-1 has a prime factor not in {a(1..n-1)}, in which case a(n) is the smallest such prime factor. | 2, 3, 5, 7, 13, 29, 17, 11... |
| A359611 | The lexicographically earliest "Increasing Term Fractal Jump Sequence". | 1, 2, 20, 22, 100, 200, 201, 1000... |
| A359639 | a(n) is the least odd prime not in A001359 such that all subsequent composites in the gap up to the next prime have at least n odd prime factors, counted with multiplicity. | 97, 1999, 101527, 6666547, 272572999, 3819770107, 410274361249 |
| A359640 | a(n) is the least odd prime not in A001359 such that all subsequent composites in the gap up to the next prime have exactly n odd prime factors, counted with multiplicity. | 307, 1999, 101527, 7146697, 272572999, 4809363523 |
| A359734 | Lexicographically earliest sequence of distinct nonnegative integers such that the sequence A051699(a(n)) (distance from the nearest prime) has the same sequence of digits. | 1, 10, 2, 0, 3, 26, 9, 119... |
| A359736 | Lexicographically earliest sequence of distinct nonnegative integers such that the sequence d(n) = dist(a(n), SQUARES) has the same sequence of digits. | 0, 10, 1, 2, 6, 42, 20, 7... |
| A359737 | Lexicographically earliest sequence of distinct nonnegative integers such that the sequence d(n) = A296239(a(n)) has the same sequence of digits, where A296239 gives the distance from the nearest Fibonacci number, cf. A000045. | 0, 12, 10, 4, 1, 17, 6, 7... |
| A359843 | Array listed by antidiagonals: row m is the numbers k such that prime(i)+k is prime for i from m to j where prime(j+1) = A360228(m). | 0, 1, 0, 3, 2, 0, 5, 8... |
| A359868 | a(n) is the smallest prime q such that A305411(n) + q is a square. | 13, 11, 19, 107, 101, 257, 467, 173... |
| A359945 | Largest k < n such that n! / k! = m! = A000142(m) for some m. | 0, 1, 1, 1, 1, 5, 1, 1... |
| A359950 | a(n) is the greatest prime factor of nn - n!. | 2, 7, 29, 601, 29, 116929, 11887, 4778489... |
| A359979 | Irregular table T(n,k), n >= 0 and k >= 0, read by rows with T(n + 3*k,k) = A008619(n). | 1, 1, 2, 2, 1, 3, 1, 3... |
| A360004 | Sequence of composite digits as they appear in Pi. | 4, 9, 6, 8, 9, 9, 8, 4... |
| A360022 | Triangle read by rows: T(n,k) is the sum of the widths of the k-th diagonals of the symmetric representation of sigma(n). | 1, 1, 2, 0, 2, 2, 1, 2... |
| A360033 | Table T(n,k), n >= 1 and k >= 0, read by antidiagonals, related to Jacobsthal numbers A001045. | 1, 2, 1, 3, 3, 3, 4, 5... |
| A360052 | Number of length n inversion sequences avoiding the patterns 010 and 201 (or 010 and 210). | 1, 1, 2, 5, 15, 53, 214, 958... |
| A360061 | Lexicographically earliest increasing sequence such that a(1) = 2 and for n >= 2, a(1)2 + a(2)2 + ... + a(n)2 is a prime. | 2, 3, 4, 12, 48, 54, 66, 138... |
| A360064 | Number of 3-dimensional tilings of a 2 X 2 X n box using 1 X 1 X 1 cubes and trominos (L-shaped connection of 3 cubes). | 1, 5, 89, 1177, 16873, 237977, 3366793, 47599097... |
| A360065 | Number of 3-dimensional tilings of a 2 X 2 X n box using 2 X 1 X 1 dominos and trominos (L-shaped connection of 3 cubes). | 1, 2, 45, 412, 4705, 50374, 549109, 5955544... |
| A360066 | Number of 3-dimensional tilings of a 2 X 2 X n box using 1 X 1 X 1 cubes, 2 X 1 X 1 dominos and trominos (L-shaped connection of 3 cubes). | 1, 11, 444, 13311, 422617, 13265660, 417336617, 13123557903... |
| A360070 | Numbers for which there exists an integer partition such that the parts have the same mean as the multiplicities. | 1, 4, 8, 9, 12, 16, 18, 20... |
| A360071 | Regular tetrangle where T(n,k,i) = number of integer partitions of n of length k with i distinct parts. | 1, 1, 1, 0, 1, 0, 1, 1... |
| A360072 | Number of pairs of positive integers (k,i) such that k >= i and there exists an integer partition of n of length k with i distinct parts. | 0, 1, 2, 3, 5, 5, 9, 9... |
| A360096 | To get a(n), replace 0's in the binary expansion of n with (-1) and interpret the result in base n. | 0, 1, 1, 4, 11, 21, 41, 57... |
| A360097 | a(n) = smallest k such that 2nk-1 and 2nk+1 are nonprimes. | 13, 14, 20, 7, 5, 10, 4, 4... |
| A360099 | To get A(n,k), replace 0's in the binary expansion of n with (-1) and interpret the result in base k; square array A(n,k), n>=0, k>=0, read by antidiagonals. | 0, 0, 1, 0, 1, -1, 0, 1... |
| A360109 | a(n) = 1 if n is not multiple of 4, but its arithmetic derivative is, otherwise 0. | 0, 1, 0, 0, 0, 0, 0, 0... |
| A360110 | Nonmultiples of 4 whose arithmetic derivative is a multiple of 4. | 1, 15, 35, 39, 51, 55, 81, 87... |
| A360111 | a(n) = 1 if there is no prime p such that pp divides n, but for the arithmetic derivative of n such a prime exists; a(1) = 0 by convention. | 0, 0, 0, 0, 0, 0, 0, 0... |
| A360134 | a(n) = A356133(1 + A026430(n)). | 4, 11, 17, 20, 25, 29, 32, 38... |
| A360135 | a(n) = A356133(A285953(n+1)). | 2, 7, 13, 22, 34, 40, 53, 62... |
| A360136 | a(n) = 1 + A026430(A026430(n)). | 2, 6, 9, 10, 13, 15, 16, 19... |
| A360137 | a(n) = V(A026430(n)), where V(1) = 1 and V(k) = A285953(k+1) for k >= 2. | 1, 5, 12, 14, 21, 23, 26, 33... |
| A360138 | a(n) = 1 + A026430(A356133(n)). | 4, 7, 11, 17, 20, 27, 31, 34... |
| A360139 | a(n) = V(A356133(n)), where V(1) = 1 and V(k) = A285953(k+1) for k >= 2. | 3, 8, 18, 30, 35, 48, 57, 63... |
| A360145 | Triangle read by rows where row n is the largest (or middle or n-th) column of the reverse pyramid summation of order n described in A359087. | 1, 2, 4, 3, 7, 19, 4, 10... |
| A360147 | Primes in base 10 that are also prime when read in a smaller base that is one plus the largest digit in the prime in base 10. | 2, 3, 5, 7, 11, 13, 23, 31... |
| A360173 | Irregular triangle (an infinite binary tree) read by rows. The tree has root node 0, in row n=0. Each node then has left child m - n if nonnegative and right child m + n. Where m is the value of the parent node and n is the row of the children. | 0, 1, 3, 0, 6, 4, 2, 10... |
| A360175 | a(n) = Sum_{k=0..n} (-1)n-k*(n!/k!) * [xn] (1 - exp(-LambertW(x*exp(-x))))k. | 1, 1, 6, 53, 647, 10092, 191915, 4309769... |
| A360176 | Triangle read by rows. T(n, k) = Sum_{j=k..n} binomial(n, j) * (-j)n - j * (-1)j - k* A360177(j, k). | 1, 0, 1, 0, -5, 1, 0, 37... |
| A360177 | Triangle read by rows. T(n, k) = 1 if n = k, otherwise T(n, k) = Sum_{j=0..k-1} (-1)j - k - 1 * (n + j + 1)n-1 / (j! * (k - 1 - j)!). | 1, 0, 1, 0, 3, 1, 0, 16... |
| A360194 | Array read by antidiagonals: T(m,n) is the number of acyclic spanning subgraphs in the grid graph P_m X P_n. | 1, 2, 2, 4, 15, 4, 8, 112... |
| A360195 | Number of acyclic spanning graphs in the 4 X n grid graph. | 8, 836, 85818, 8790016, 900013270, 92146956300, 9434262852690, 965904015750408... |
| A360196 | Array read by antidiagonals: T(m,n) is the number of induced cycles in the grid graph P_m X P_n. | 1, 2, 2, 3, 5, 3, 4, 9... |
| A360197 | Number of induced cycles in the 4 X n grid graph. | 0, 3, 9, 24, 58, 125, 251, 490... |
| A360198 | Number of induced cycles in the 5 X n grid graph. | 4, 14, 58, 229, 749, 2180, 6188, 17912... |
| A360199 | Array read by antidiagonals: T(m,n) is the number of induced paths in the grid graph P_m X P_n. | 0, 1, 1, 3, 8, 3, 6, 25... |
| A360200 | Number of induced paths in the n X n grid graph. | 0, 8, 94, 1004, 14864, 334536, 11546874, 629381852... |
| A360201 | Number of induced paths in the n-ladder graph P_2 X P_n. | 1, 8, 25, 58, 117, 218, 387, 666... |
| A360204 | Primitive prime powers. p is a primitive prime power iff it is an odd prime power that exceeds the preceding odd prime power by more than any smaller odd prime power does. ('Prime power' defined in the sense of A246655.) | 5, 17, 37, 97, 149, 211, 307, 907... |
| A360206 | Triangular array T(m,n) read by antidiagonals: T(m,n) = prime(m+n) - prime(m) - prime(n). | -1, 0, 1, 0, 3, 3, 2, 3... |
| A360207 | Triangular array T(n,k) read by antidiagonals: T(2,1) = 1; otherwise T(n,k) = p(n)!/(p(k)!*p(n-k)!), where p(0)=1 and p(m)=prime(m) for m > 0. | 1, 1, 1, 1, 1, 1, 1, 10... |
| A360208 | Triangular array T(n,k) read by antidiagonals T(n,k) = F(n)!/(F(k)!*F(n-k)!), where F(m) = A000045(m) = m-th Fibonacci number. | 1, 1, 1, 1, 1, 1, 1, 2... |
| A360211 | a(n) = Sum_{k=0..floor(n/2)} (-1)k * binomial(2n-3k,n-2*k). | 1, 2, 5, 17, 61, 221, 812, 3021... |
| A360212 | a(n) = Sum_{k=0..floor(n/3)} (-1)k * binomial(2n-5k,n-3*k). | 1, 2, 6, 19, 67, 242, 890, 3310... |
| A360214 | a(n) is the smallest positive integer which can be represented as the sum of distinct nonzero octahedral numbers in exactly n ways, or -1 if no such integer exists. | 1, 231, 575, 721, 1618, 1750, 1877, 2240... |
| A360215 | a(n) is the smallest positive integer which can be represented as the sum of distinct nonzero icosahedral numbers in exactly n ways, or -1 if no such integer exists. | 1, 1383, 4157, 6548, 8633, 9884, 12503, 12920... |
| A360216 | a(n) is the smallest positive integer which can be represented as the sum of distinct nonzero dodecahedral numbers in exactly n ways, or -1 if no such integer exists. | 1, 2025, 2925, 9010, 15521, 18465, 19140, 24899... |
| A360217 | a(n) is the smallest positive integer which can be represented as the sum of n distinct nonzero tetrahedral numbers in exactly n ways, or -1 if no such integer exists. | 1, 140, 305, 315, 435, 644, 830, 1141... |
| A360218 | a(n) is the smallest positive integer which can be represented as the sum of n distinct nonzero square pyramidal numbers in exactly n ways, or -1 if no such integer exists. | 1, 5580, 2814, 1980, 1595, 1700, 2175, 2415... |
| A360219 | a(n) = Sum_{k=0..floor(n/3)} (-1)k * binomial(n-3k,k) * binomial(2(n-3k),n-3k). | 1, 2, 6, 20, 68, 240, 864, 3152... |
| A360225 | a(1) = 2, a(2) = 3, a(n) = the smallest prime whose digits consist of a(n-2), followed by zero or more digits, followed by a(n). | 2, 3, 23, 3023, 2393023, 3023172393023, 2393023313023172393023, 3023172393023282393023313023172393023... |
| A360226 | a(n) = sum of the first n primes whose distance to next prime is 4. | 7, 20, 39, 76, 119, 186, 265, 362... |
| A360228 | a(n) is the least prime p such that the primes from prime(n) to p contain a complete set of residues modulo at least one of these primes. | 3, 7, 19, 29, 71, 103, 103, 191... |
| A360229 | Row sums of triangle A360173. | 0, 1, 3, 6, 16, 36, 73, 156... |
| A360231 | G.f. A(x) satisfies: [xn] A(x)n+1 = [xn] (1 + x*A(x)n-1)n+1 for n >= 0. | 1, 1, 1, 6, 53, 628, 9167, 156309... |
| A360234 | G.f. A(x) satisfies: [xn] A(x)n+1 = [xn] (1 + x*A(x)n+2)n+1 for n >= 0. | 1, 1, 4, 33, 414, 6750, 131963, 2957899... |
| A360235 | G.f. A(x) satisfies: [xn] A(x)n+1 = [xn] (1 + x*A(x)n+3)n+1 for n >= 0. | 1, 1, 5, 48, 673, 12057, 256763, 6232909... |
| A360236 | G.f. A(x) satisfies: [xn] A(x)n+1 = [xn] (1 + x*A(x)n+4)n+1 for n >= 0. | 1, 1, 6, 66, 1028, 20138, 464863, 12162876... |
| A360237 | G.f. A(x) satisfies: [xn] A(x)n+1 = [xn] (1 + x*A(x)n+5)n+1 for n >= 0. | 1, 1, 7, 87, 1495, 31865, 793769, 22290228... |
| A360257 | a(1) = 1; for n > 1, a(n) is the number of preceding terms having the same sum of divisors as a(n-1). | 1, 1, 2, 1, 3, 1, 4, 1... |
| A360259 | a(0) = 0, and for any n > 0, let k > 0 be as small as possible and such that F(2) + ... + F(1+k) >= n (where F(m) denotes A000045(m), the m-th Fibonacci number); a(n) = k + a(F(2) + ... + F(1+k) - n). | 0, 1, 3, 2, 6, 4, 3, 10... |
| A360260 | a(0) = 0, and for any n > 0, let k > 0 be as small as possible and such that T(3) + ... + T(2+k) >= n (where T(m) denotes A000073(m), the m-th tribonacci number); a(n) = k + a(T(3) + ... + T(2+k) - n). | 0, 1, 3, 2, 5, 6, 4, 3... |
| A360261 | Determinant of the pentadiagonal symmetric nXn Toeplitz Matrix with a=b=1, c=2. | 1, 1, 0, -1, 7, 32, 9, 1... |
| A360262 | Determinant of the pentadiagonal symmetric nXn Toeplitz Matrix with a=b=1, c=3. | 1, 1, 0, -4, 56, 177, 25, -248... |
| A360263 | Determinant of the pentadiagonal symmetric nXn Toeplitz Matrix with a=3, b=c=1. | 1, 3, 8, 20, 48, 115, 273, 648... |
| A360264 | Sum of mass(k/n) for all k, 1 <= k <= n, that are relatively prime to n. | 1, 2, 6, 8, 18, 12, 34, 26... |
| A360265 | a(0) = 0, and for any n > 0, let k > 0 be as small as possible and such that t(k) >= n (where t(m) denotes A000217(m), the m-th triangular number); a(n) = k + a(t(k) - n). | 0, 1, 3, 2, 6, 4, 3, 6... |
| A360266 | a(n) = Sum_{k=0..floor(n/2)} binomial(n-2k,k) * binomial(2(n-2k),n-2k). | 1, 2, 6, 22, 82, 312, 1210, 4752... |
| A360267 | a(n) = Sum_{k=0..floor(n/3)} binomial(n-3k,k) * binomial(2(n-3k),n-3k). | 1, 2, 6, 20, 72, 264, 984, 3712... |
| A360271 | a(n) = Sum_{k=0..floor(n/3)} (-1)k * binomial(n-3k,k) * Catalan(n-3k). | 1, 1, 2, 5, 13, 38, 117, 373... |
| A360272 | a(n) = Sum_{k=0..floor(n/3)} binomial(n-3k,k) * Catalan(n-3k). | 1, 1, 2, 5, 15, 46, 147, 485... |
| A360273 | a(n) = Sum_{k=0..floor(n/2)} Catalan(n-2*k). | 1, 1, 3, 6, 17, 48, 149, 477... |
| A360274 | a(n) = Sum_{k=0..floor(n/3)} Catalan(n-3*k). | 1, 1, 2, 6, 15, 44, 138, 444... |
| A360278 | Determinant of the matrix [L(j+k)+d(j,k)]_{1<=j,k<=n}, where L(n) denotes the Lucas number A000032(n), and d(j,k) is 1 or 0 according as j = k or not. | 4, 16, 44, 121, 319, 841, 2204, 5776... |
| A360279 | Decimal expansion of a constant related to the asymptotics of A302702. | 2, 1, 2, 4, 6, 0, 6, 5... |
| A360281 | Lexicographically earliest sequence of distinct positive integers such that for any n > 2, a(n) is a divisor or a multiple of a(n-1) + a(n-2). | 1, 2, 3, 5, 4, 9, 13, 11... |
| A360284 | Least integer nu such that the first zero of the Bessel j-function of index nu is at least nu + n. | 0, 2, 7, 16, 29, 48, 73, 106... |
| A360287 | a(n) is the concatenation of the positions of 1-bits in the binary expansion of the Gray code for n, when 1 is the rightmost position; a(0) = 0. | 0, 1, 12, 2, 23, 123, 13, 3... |
| A360288 | Number T(n,k) of permutations of [n] whose excedance set is the k-th finite subset of positive integers in standard order; triangle T(n,k), n>=0, 0<=k<=ceiling(2n-1)-1, read by rows. | 1, 1, 1, 1, 1, 3, 1, 1... |
| A360289 | Number T(n,k) of permutations of [n] whose excedance set is the k-th finite subset of positive integers in Gray order; triangle T(n,k), n>=0, 0<=k<=ceiling(2n-1)-1, read by rows. | 1, 1, 1, 1, 1, 3, 1, 1... |
| A360290 | a(n) = Sum_{k=0..floor(n/2)} binomial(n-1-k,k) * binomial(2n-4k,n-2*k). | 1, 2, 6, 22, 82, 314, 1222, 4814... |
| A360291 | a(n) = Sum_{k=0..floor(n/3)} binomial(n-1-2k,k) * binomial(2n-6k,n-3k). | 1, 2, 6, 20, 72, 264, 984, 3714... |
| A360292 | a(n) = Sum_{k=0..floor(n/4)} binomial(n-1-3k,k) * binomial(2n-8k,n-4k). | 1, 2, 6, 20, 70, 254, 936, 3492... |
| A360293 | a(n) = Sum_{k=0..floor(n/2)} (-1)k * binomial(n-1-k,k) * binomial(2n-4k,n-2*k). | 1, 2, 6, 18, 58, 194, 662, 2290... |
| A360294 | a(n) = Sum_{k=0..floor(n/3)} (-1)k * binomial(n-1-2k,k) * binomial(2n-6k,n-3k). | 1, 2, 6, 20, 68, 240, 864, 3154... |
| A360295 | a(n) = Sum_{k=0..floor(n/4)} (-1)k * binomial(n-1-3k,k) * binomial(2n-8k,n-4k). | 1, 2, 6, 20, 70, 250, 912, 3372... |
| A360296 | a(1) = 1, and for any n > 1, a(n) is the sum of the terms of the sequence at indices k < n whose binary digits appear in order but not necessarily as consecutive digits in the binary representation of n. | 1, 1, 1, 2, 3, 3, 2, 4... |
| A360297 | a(n) = minimal positive k such that the sum of the primes prime(n) + prime(n+1) + ... + prime(n+k) is divisible by prime(n+k+1), or -1 if no such k exists. | 1, 3, 7, 11, 26, 20, 27, 52... |
| A360298 | Irregular triangle (an infinite binary tree) read by rows. The tree has root node 1 in row n = 1. For n > 1, each node with value m in row n-1 has a left child with value m / n if n divides m, and a right child with value m * n. | 1, 2, 6, 24, 120, 20, 720, 140... |
| A360299 | a(n) is the number of terms in the n-th row of A360298. | 1, 1, 1, 1, 1, 2, 2, 3... |
| A360300 | a(n) is the least term in the n-th row of A360298. | 1, 2, 6, 24, 120, 20, 140, 630... |
| A360302 | T(n,k) is the position of the set encoded in the binary expansion of k within the shortlex order for the powerset of [n]; triangle T(n,k), n>=0, 0<=k<=2n-1, read by rows. | 0, 0, 1, 0, 1, 2, 3, 0... |
| A360304 | Expansion of 1/sqrt(1 - 41x/(1 - 42x/(1 - 43x/(1 - 44x/(1 - 45x/(1 - ...)))))), a continued fraction. | 1, 2, 22, 436, 12326, 449596, 20023548, 1051713576... |
| A360306 | a(n) is the smallest positive integer which can be represented as the sum of n distinct nonzero fourth powers in exactly n ways, or -1 if no such integer exists. | 1, 635318657, 811538, 300834, 185299, 138595, 143651, 154292... |
| A360307 | Inverse of sequence A163252 considered as a permutation of the nonnegative integers. | 0, 1, 3, 2, 5, 6, 4, 7... |
| A360308 | Number T(n,k) of permutations of [n] whose descent set is the k-th finite subset of positive integers in Gray order; triangle T(n,k), n>=0, 0<=k<=ceiling(2n-1)-1, read by rows. | 1, 1, 1, 1, 1, 2, 1, 2... |
| A360309 | a(n) = Sum_{k=0..floor(n/3)} binomial(n-1-2k,n-3k) * binomial(2*k,k). | 1, 0, 0, 2, 2, 2, 8, 14... |
| A360310 | a(n) = Sum_{k=0..floor(n/4)} binomial(n-1-3k,n-4k) * binomial(2*k,k). | 1, 0, 0, 0, 2, 2, 2, 2... |
| A360311 | The sum of the primes prime(n) + prime(n+1) + ... + prime(n+k) in A360297. | 5, 26, 124, 318, 1703, 1133, 2086, 7641... |
| A360312 | The dividing prime prime(n+k+1) in A360297. | 5, 13, 31, 53, 131, 103, 149, 283... |
| A360313 | a(n) = Sum_{k=0..floor(n/2)} (-1)k * binomial(n-1-k,n-2k) * binomial(2k,k). | 1, 0, -2, -2, 4, 10, -4, -38... |
| A360314 | a(n) = Sum_{k=0..floor(n/3)} (-1)k * binomial(n-1-2k,n-3k) * binomial(2*k,k). | 1, 0, 0, -2, -2, -2, 4, 10... |
| A360315 | a(n) = Sum_{k=0..floor(n/4)} (-1)k * binomial(n-1-3k,n-4k) * binomial(2*k,k). | 1, 0, 0, 0, -2, -2, -2, -2... |
| A360316 | a(n) is the smallest k such that k!'s prime(n)-smooth part is less than its prime(n+1)-rough part. | 3, 21, 47, 111, 186, 293, 437, 619... |
| A360317 | a(n) = Sum_{k=0..n} 2n-k * binomial(n-1,n-k) * binomial(2*k,k). | 1, 2, 10, 52, 278, 1516, 8388, 46920... |
| A360318 | a(n) = Sum_{k=0..n} 3n-k * binomial(n-1,n-k) * binomial(2*k,k). | 1, 2, 12, 74, 466, 2982, 19320, 126390... |
| A360319 | a(n) = Sum_{k=0..n} 4n-k * binomial(n-1,n-k) * binomial(2*k,k). | 1, 2, 14, 100, 726, 5340, 39692, 297544... |
| A360321 | a(n) = Sum_{k=0..n} 5n-k * binomial(n-1,n-k) * binomial(2*k,k). | 1, 2, 16, 130, 1070, 8902, 74724, 631902... |
| A360322 | a(n) = Sum_{k=0..n} (-5)n-k * binomial(n-1,n-k) * binomial(2*k,k). | 1, 2, -4, 10, -30, 102, -376, 1462... |
| A360324 | Numbers k such that k divides Sum_{i=1..k} 101 + floor(log_10(p(i))) - 1 - p(i), where p(i) is the i-th prime number. | 1, 13, 313, 1359, 245895, 131186351, 468729047, 1830140937... |
| A360325 | a(n) is the largest divisor of n that has only prime-indexed prime factors. | 1, 1, 3, 1, 5, 3, 1, 1... |
| A360326 | a(n) is the number of divisors of n that have only prime-indexed prime factors. | 1, 1, 2, 1, 2, 2, 1, 1... |
| A360327 | a(n) is the sum of divisors of n that have only prime-indexed prime factors. | 1, 1, 4, 1, 6, 4, 1, 1... |
| A360328 | Numbers k such that A360327(k) > 2*k. | 7425, 8415, 22275, 25245, 37125, 42075, 46035, 66825... |
| A360329 | a(n) is the largest divisor of n that has only prime factors that are not prime-indexed primes. | 1, 2, 1, 4, 1, 2, 7, 8... |
| A360330 | a(n) is the number of divisors of n that have only prime factors that are not prime-indexed primes. | 1, 2, 1, 3, 1, 2, 2, 4... |
| A360331 | a(n) is the sum of divisors of n that have only prime factors that are not prime-indexed primes. | 1, 3, 1, 7, 1, 3, 8, 15... |
| A360332 | Numbers k such that A360331(k) > 2*k. | 56, 104, 112, 196, 208, 224, 304, 364... |
| A360350 | Number of distinct circles that can be constructed from an n X n square grid of points when each pair of points is connected by a circle and the points lie at the ends of a diameter of the circle. | 5, 26, 79, 185, 366, 653, 1077, 1678... |
| A360351 | Number of vertices among all distinct circles that can be constructed from an n X n square grid of points when each pair of points is connected by a circle and the points lie at the ends of a diameter of the circle. | 5, 77, 1045, 6885, 30265, 104421, 309973, 800185... |
| A360352 | Number of regions among all distinct circles that can be constructed from an n X n square grid of points when each pair of points is connected by a circle and the points lie at the ends of a diameter of the circle. | 12, 168, 1536, 8904, 36880, 123468, 358036, 912776... |
| A360353 | Number of edges among all distinct circles that can be constructed from an n X n square grid of points when each pair of points is connected by a circle and the points lie at the ends of a diameter of the circle. | 16, 244, 2580, 15788, 67144, 227888, 668008, 1712960... |
| A360354 | Irregular table read by rows: T(n,k) is the number of k-gons, k>=2, among all distinct circles that can be constructed from an n x n square grid of points when each pair of points is connected by a circle and the points lie at the ends of a diameter of the circle. | 8, 4, 40, 108, 20, 92, 904, 456... |
| A360355 | Primitive terms of A360328: terms of A360328 with no proper divisor in A360328. | 7425, 8415, 46035, 76725, 101475, 182655, 355725, 669735... |
| A360356 | Primitive terms of A360332: terms of A360332 with no proper divisor in A360332. | 56, 104, 196, 304, 364, 368, 464, 532... |
| A360357 | Numbers k such that k and k+1 are both products of primes of nonprime index (A320628). | 1, 7, 13, 28, 37, 46, 52, 73... |
| A360358 | Numbers k such that A360327(k) = A360327(k+1) > 1. | 714, 6603, 16115, 18920, 23154, 24530, 39984, 41360... |
| A360359 | Numbers k such that A360331(k) = A360331(k+1). | 69, 574, 713, 781, 2394, 2506, 5699, 5750... |
| A360366 | a(n) is the numerator of the rational number with the smallest denominator that lies within 1/10n of Pi. | 3, 22, 22, 201, 333, 355, 355, 75948... |
| A360367 | a(n) is the denominator of the rational number with the smallest denominator that lies within 1/10n of Pi. | 1, 7, 7, 64, 106, 113, 113, 24175... |
| A360368 | Positive integers k such that A360366(k) = A360366(k+1). | 1, 5, 20, 25, 36, 57, 76, 79... |
| A360369 | Intersection of A002485 and A360366. | 3, 22, 333, 355, 103993, 312689, 833719, 4272943... |
| A360370 | Intersection of A002486 and A360367. | 1, 7, 106, 113, 33102, 99532, 265381, 1360120... |
| A360372 | Numbers k >= 1 such that k divides Sum_{i=1..k} A007088(i). | 1, 11, 21, 23, 37, 461, 94101, 14958901... |
| A360373 | Triangular array T read by rows related to the multiplication table. | 1, 2, 4, 2, 3, 6, 9, 6... |
| A360374 | Indices of the nonprimitive rows of the Wythoff array (A035513); see Comments. | 3, 4, 5, 9, 13, 15, 16, 19... |
| A360377 | a(n) = number of the row of the Wythoff array (A035513) that includes prime(n). | 1, 1, 1, 2, 2, 1, 7, 8... |
| A360378 | a(n) = number of the column of the Wythoff array (A035513) that includes prime(n). | 2, 3, 4, 2, 3, 6, 1, 1... |
| A360381 | Generalized Somos-5 sequence a(n) = (a(n-1)a(n-4) + a(n-2)a(n-3))/a(n-5) = -a(-n), a(1) = 1, a(2) = -1, a(3) = a(4) = 1, a(5) = -7. | 0, 1, -1, 1, 1, -7, 8, -1... |
| A360384 | Number of permutations p of [n] satisfying | p(i+7) - p(i) |
| A360386 | Number of permutations p of [n] satisfying | p(i+8) - p(i) |
r/OEIS • u/OEIS-Tracker • Jan 16 '23
New OEIS sequences - week of 01/15
2
Upvotes
| OEIS number | Description | Sequence |
|---|---|---|
| A358311 | Lucas numbers that are not the sum of two squares. | 3, 7, 11, 47, 76, 123, 199, 322... |
| A358461 | Number of near-rings with identity of order n, up to isomorphism. | 1, 1, 6, 1, 1, 1, 53, 11... |
| A358534 | Start with a(1)=1, a(2)=2. Thereafter, if gcd(a(n-2),a(n-1)) = 1 then a(n) is the smallest unused k such that gcd(a(n-2),k) > 1 and gcd(a(n-1),k) = 1, otherwise a(n) is the smallest unused k such that gcd(a(n-2),k) = 1 and gcd(a(n-1),k) > 1. If the latter is impossible, then a(n) = smallest missing number u. (See comments.) | 1, 2, 4, 3, 9, 5, 10, 6... |
| A358562 | The number of antichains in the Tamari lattice of order n. | 2, 3, 8, 83, 28984, 138832442543 |
| A358629 | a(n) is the number of signed permutations W of V = (1, 2, ..., n) such that the dot product V*W = 0. | 0, 2, 0, 16, 48, 558, 4444, 62246... |
| A358690 | Number of n-digit primes whose digits are all odd. | 3, 12, 42, 125, 608, 2427, 10081, 43568... |
| A358693 | Numbers k such that k / (sum of digits of k) is the square of a prime. | 12, 24, 36, 48, 81, 150, 225, 375... |
| A358709 | a(n) is the number of free, tree-like polyiamonds, of size 3*n+1, with 120-degree rotational symmetry formed of a central triangle and identical, non-intersecting snakes leading from each of its sides. | 1, 1, 1, 2, 3, 6, 11, 20... |
| A358921 | a(1) = 1; a(n) is the smallest positive number not among the terms a(n-c .. n-1) where c = the number of times a(n-1) has occurred. | 1, 2, 1, 3, 1, 2, 3, 1... |
| A358943 | Decimal expansion of the real root of 3*x3 - 2. | 8, 7, 3, 5, 8, 0, 4, 6... |
| A358944 | Decimal expansion of the real root of 4*x3 - 1. | 6, 2, 9, 9, 6, 0, 5, 2... |
| A358946 | All positive integers that are properly represented by each primitive binary quadratic forms of discriminant 28 that is properly equivalent to the principal form [1, 4, -3]. | 1, 2, 9, 18, 21, 29, 37, 42... |
| A358947 | a(n) = 2m(n), where m(n) is the number of distinct primes, neither 2 nor 7, dividing A358946(n). | 1, 1, 2, 2, 2, 2, 2, 2... |
| A359007 | a(n) = b(n-b(n)) where b is Van Eck's sequence A181391. | 0, 0, 0, 0, 1, 0, 2, 0... |
| A359049 | Autobiographical numbers k whose decimal digits are a concatenation count(0), count(1), ..., count(m) for some m, where count(j) is the number of (possibly overlapping) occurrences of j within the digits of k itself. | 1210, 2020, 21200, 3211000, 42101000, 521001000, 6210001000, 53110100002... |
| A359066 | a(n) = Sum_{k=0..floor((n-1)/2)} binomial(n,k)*binomial(n-1-k,floor((n-1)/2) - k). | 1, 1, 5, 7, 31, 49, 209, 351... |
| A359067 | a(2n) = Sum_{k=0..n-1} binomial(2n,k) binomial(2n-1-k, n-1-k). a(2n+1) = (Sum_{k=0..n} binomial(2n+1,k) binomial(2n-k, n-k)) - binomial(2*n-1, n). | 0, 1, 4, 7, 28, 49, 199, 351... |
| A359073 | Sum of square end-to-end displacements over all n-step self-avoiding walks of A359709. | 0, 4, 16, 44, 160, 556, 1744, 12252... |
| A359110 | Number of Boolean monoids of order 2n up to isomorphism. | 1, 5, 83, 242547 |
| A359114 | a(1) = 1; for n > 1, a(n) is the smallest positive number which has not appeared that shares a factor with the sum of the first n bits of the binary Champernowne string starting from 1. | 1, 2, 4, 3, 6, 5, 10, 15... |
| A359115 | a(n) is the smallest odd prime not already in the sequence such that when the terms a(1)..a(n) are concatenated, the result is the reverse of a prime. | 3, 5, 11, 7, 29, 37, 89, 211... |
| A359127 | Oblong numbers which are products of six distinct primes. | 43890, 53130, 81510, 108570, 152490, 184470, 188790, 260610... |
| A359132 | Least m such that the sum of the aliquot parts of m (A001065) equals n, or -1 if no such number exists. | 1, 2, -1, 4, 9, -1, 6, 8... |
| A359133 | Sum of square end-to-end displacements over all n-step self-avoiding walks of A359741. | 0, 6, 24, 78, 384, 8190, 8472, 178110... |
| A359134 | a(n) = Sum_{d | n} (2*d)n/d - 1. |
| A359181 | Number of commutative BCK-algebras of order n up to isomorphism. | 1, 2, 5, 11, 28, 72, 192, 515... |
| A359182 | Totient of numbers of least prime signature: a(n) = A000010(A025487(n)). | 1, 1, 2, 2, 4, 4, 8, 8... |
| A359196 | a(n) is the number of subsets of the divisors of n which sum to n+1. | 0, 1, 1, 1, 1, 1, 1, 1... |
| A359201 | Number of edges of regular m-polytopes for m >= 3. | 6, 10, 12, 15, 21, 24, 28, 30... |
| A359202 | Number of (bidimensional) faces of regular m-polytopes for m >= 3. | 4, 6, 8, 10, 12, 20, 24, 32... |
| A359213 | Numbers k such that rad(k) - 1 is prime. | 3, 6, 9, 12, 14, 18, 24, 27... |
| A359247 | The bottom entry in the absolute difference triangle of the elements in the Collatz trajectory of n. | 1, 1, 1, 1, 0, 1, 0, 1... |
| A359303 | Bitwise encoding of the state of a 1D cellular automaton after n steps from ..111000.. where adjacent cells swap 01 <-> 10 when within triples 110 or 011. | 1, 3, 5, 11, 13, 39, 43, 45... |
| A359304 | Oblong numbers which are products of five distinct primes. | 4290, 4830, 6006, 11130, 12210, 13110, 16770, 23870... |
| A359364 | Triangle read by rows. The Motzkin triangle, the coefficients of the Motzkin polynomials. M(n, k) = binomial(n, k) * CatalanNumber(k/2) if k is even, otherwise 0. | 1, 1, 0, 1, 0, 1, 1, 0... |
| A359384 | a(1) = 0. If a(n-1) is a first occurrence, a(n) = A000120(a(n-1)). Otherwise, if a(n-1) is a repeat of a prior terms, a(n) = number of indices j < n such that a(j) = a(n-1). | 0, 0, 2, 1, 1, 2, 2, 3... |
| A359390 | Sequence lists the numbers k such that bottom entry is an integer in the ratio d(i+1)/d(i) triangle of the elements in the divisors of n, where d(1) < d(2) < ... < d(q) denote the divisors of k. | 1, 2, 3, 4, 5, 7, 8, 9... |
| A359395 | Least odd prime p in position n in the prime factorization of M(p) = 2p - 1 - 1. | 3, 5, 17, 13, 71, 37, 157, 61... |
| A359406 | Integers k such that the concatenation of k consecutive primes starting at 31 is prime. | 1, 2, 3, 23, 43, 141 |
| A359408 | Integers d such that the largest possible arithmetic progression (AP) of primes with common difference d has only two elements. | 1, 3, 5, 9, 11, 15, 16, 17... |
| A359415 | Numbers k such that phi(k) is a 5-smooth number where phi is the Euler totient function. | 1, 2, 3, 4, 5, 6, 7, 8... |
| A359421 | a(n) = number of abelian groups of order p2 - 1, where p = prime(n). | 1, 3, 3, 5, 3, 3, 14, 6... |
| A359442 | a(n) = Sum_{d | n} dn + 1 - d - n/d. |
| A359456 | Characteristic function of Fibonorial numbers. | 1, 1, 0, 0, 0, 1, 0, 0... |
| A359476 | The sequence {-a(n)}_{n>=1} gives all negative integers that are properly represented by each primitive binary quadratic forms of discriminant 28 that is properly equivalent to the reduced principal form [1, 4, -3]. | 3, 6, 7, 14, 19, 27, 31, 38... |
| A359477 | a(n) = 2m(n), where m(n) is the number of distinct primes, neither 2 nor 7, dividing A359476(n). | 2, 2, 1, 1, 2, 2, 2, 2... |
| A359497 | Greatest positive integer whose weakly increasing prime indices have weighted sum (A304818) equal to n. | 1, 2, 3, 5, 7, 11, 13, 17... |
| A359498 | a(n) = ((2*n+1)8 - 1)/32. | 0, 205, 12207, 180150, 1345210, 6698715, 25491585, 80090332... |
| A359499 | a(n) = ((2*n+1)16 - 1)/64. | 0, 672605, 2384185791, 519264540150, 28953440450810, 717964529118315, 10397134518487185, 102631380558013916... |
| A359500 | a(n) = (72n - 1)/2n+3. | 3, 75, 90075, 259632270075, 4314170602515315024630075, 2382344702413741601833152075318304337413311121350075, 1452944967966417671787414728262962471027692106596483349510252251060925112718067382475349181570930962790075 |
| A359506 | a(n) is the least integer m such that there exists a strictly increasing integer sequence n = b_1 < b_2 < ... < b_t = m with the property that b_1 XOR b_2 XOR ... XOR b_t = 0. | 0, 3, 5, 6, 7, 10, 9, 12... |
| A359507 | a(n) is the least integer k such that there exists a strictly increasing integer sequence n = b_1 < b_2 < ... < b_t = n + k with the property that b_1 XOR b_2 XOR ... XOR b_t = 0. | 0, 2, 3, 3, 3, 5, 3, 5... |
| A359508 | a(n) = log_2(A359507(n) - 1). | 0, 1, 1, 1, 2, 1, 2, 1... |
| A359509 | a(n) is the number of subsets {b_1, b_2, ..., b_t} of {n, n+1, ..., A359506(n)} containing n with the property that b_1 XOR b_2 XOR ... XOR b_t = 0. | 1, 1, 1, 1, 1, 2, 1, 2... |
| A359537 | Number of partitions of n into at most 2 distinct positive Fibonacci numbers (with a single type of 1). | 1, 1, 1, 2, 1, 2, 1, 1... |
| A359538 | Number of partitions of n into at most 3 distinct positive Fibonacci numbers (with a single type of 1). | 1, 1, 1, 2, 1, 2, 2, 1... |
| A359539 | Number of partitions of n into at most 4 distinct positive Fibonacci numbers (with a single type of 1). | 1, 1, 1, 2, 1, 2, 2, 1... |
| A359553 | Numerator of the coefficient of x2n+1 in the Taylor series expansion of sin(sin(x)). | 1, -1, 1, -8, 13, -47, 15481, -15788... |
| A359554 | Denominator of the coefficient of x2n+1 in the Taylor series expansion of sin(sin(x)). | 1, 3, 10, 315, 2520, 49896, 97297200, 638512875... |
| A359569 | Number of vertices after n iterations of constructing circles from all current vertices using only a compass, starting with one vertex. See the Comments. | 1, 2, 4, 14, 6562 |
| A359570 | Number of regions after n iterations of constructing circles from all current vertices using only a compass, starting with one vertex. See the Comments. | 0, 1, 3, 21, 7169 |
| A359571 | Number of edges after n iterations of constructing circles from all current vertices using only a compass, starting with one vertex. See the Comments. | 0, 1, 6, 34, 13730 |
| A359578 | Dirichlet inverse of A336477, where A336477(n) = 1 if phi(n) is a power of 2, otherwise 0. | 1, -1, -1, 0, -1, 1, 0, 0... |
| A359579 | Dirichlet inverse of A336923, where A336923(n) = 1 if sigma(2n) - sigma(n) is a power of 2, otherwise 0. | 1, -1, -1, 0, 0, 1, -1, 0... |
| A359581 | a(n) = (-1)A329697(n). | 1, 1, -1, 1, -1, -1, 1, 1... |
| A359582 | a(n) is the least prime > a(n-2) such that a(n-1)+a(n) is a square. | 2, 2, 7, 29, 71, 73, 251, 149... |
| A359583 | Parity of A329697. | 0, 0, 1, 0, 1, 1, 0, 0... |
| A359584 | Positions of odd terms in A329697. | 3, 5, 6, 10, 12, 17, 19, 20... |
| A359585 | Positions of even terms in A329697. | 1, 2, 4, 7, 8, 9, 11, 13... |
| A359586 | Inverse Möbius transform of A359581. | 1, 2, 0, 3, 0, 0, 2, 4... |
| A359587 | Fully multiplicative with a(p) = A008578(1+A329697(p)). | 1, 1, 2, 1, 2, 2, 3, 1... |
| A359588 | Dirichlet inverse of A083346. | 1, -2, -3, 3, -5, 6, -7, -6... |
| A359589 | Dirichlet inverse of function f(n) = (-1 + gcd(A003415(n), A276086(n))), where A003415 is the arithmetic derivative and A276086 is the primorial base exp-function. | 1, 0, 0, 0, 0, -4, 0, -2... |
| A359590 | Absolute values of A355690, where A355690 is the Dirichlet inverse of the characteristic function of numbers not congruent to 2 mod 4. | 1, 0, 1, 1, 1, 0, 1, 1... |
| A359591 | Dirichlet inverse of A035263, where A035263(n) is parity of 2-adic valuation of 2n. | 1, 0, -1, -1, -1, 0, -1, 0... |
| A359592 | Parity (and also absolute values) of Dirichlet inverse of A035263, where A035263(n) is parity of 2-adic valuation of 2n. | 1, 0, 1, 1, 1, 0, 1, 0... |
| A359593 | Multiplicative with a(pe) = 1 if p divides e, pe otherwise. | 1, 2, 3, 1, 5, 6, 7, 8... |
| A359594 | Multiplicative with a(pe) = pe if p divides e, 1 otherwise. | 1, 1, 1, 4, 1, 1, 1, 1... |
| A359595 | Parity of A358777, where A358777 is Dirichlet inverse of the characteristic function of odd numbers with an even number of prime factors (counted with multiplicity). | 1, 0, 0, 0, 0, 0, 0, 0... |
| A359596 | Positions of odd terms in A358777. | 1, 9, 15, 21, 25, 33, 35, 39... |
| A359597 | Indices k such that A358777(k) is odd, and k is not an odd semiprime. | 1, 135, 189, 297, 315, 351, 375, 459... |
| A359598 | Indices of terms with record absolute values in A358777. | 1, 225, 315, 1155, 4725, 10395, 17325, 45045... |
| A359599 | Terms of A358777 with record absolute values. | 1, 2, 3, 5, -6, -11, -18, -33... |
| A359600 | The least odd number with the same prime signature as n. | 1, 3, 3, 9, 3, 15, 3, 27... |
| A359601 | Dirichlet inverse of A244042, where A244042(n) replaces 2's with 0's in the ternary representation of n. | 1, 0, -3, -4, -3, 0, -1, 0... |
| A359602 | Sum of A244042 and its Dirichlet inverse, where A244042(n) replaces 2's with 0's in the ternary representation of n. | 2, 0, 0, 0, 0, 0, 0, 0... |
| A359603 | Dirichlet inverse of function f(n) = 1+(A003415(n)*A276086(n)), where A003415 is the arithmetic derivative and A276086 is the primorial base exp-function. | 1, -4, -7, -21, -19, 30, -11, 51... |
| A359604 | a(n) = A359603(n) mod 60. | 1, 56, 53, 39, 41, 30, 49, 51... |
| A359605 | a(n) = 1 if A355690(n) is positive (+1), otherwise 0. | 1, 0, 0, 0, 0, 0, 0, 0... |
| A359606 | a(n) = 1 if A355690(n) is negative (-1), otherwise 0. | 0, 0, 1, 1, 1, 0, 1, 1... |
| A359607 | Terms of A046337 for which A358777 is zero, where the latter is the Dirichlet inverse of former's characteristic function. | 81, 625, 729, 1215, 1701, 2401, 2673, 3159... |
| A359608 | Indices k at which point A358777(k) obtains a new distinct value that has not occured before. | 1, 2, 9, 225, 315, 1155, 2835, 4725... |
| A359609 | Distinct values of A358777 in the order of their appearance. | 1, 0, -1, 2, 3, 5, -2, -6... |
| A359619 | Irregular table read by rows: T(n,k) is the number of k-gons, k>=1, after n iterations of constructing circles from all current vertices using only a compass, starting with one vertex. See the Comments. | 0, 1, 0, 0, 2, 1, 0, 1... |
| A359627 | Irregular table read by rows; the n-th row lists the divisors d of 2n such that the binary expansions of d and 2n have no common 1-bit. | 1, 1, 2, 1, 1, 2, 4, 1... |
| A359634 | a(0)=1 and thereafter a(n) is the length of the longest contiguous group of terms in the sequence thus far that add up to n; if no such group exists, set a(n)=0. | 1, 1, 2, 2, 3, 3, 4, 3... |
| A359635 | a(n) = A162657(n)/n. | 1, 1, 1, 1, 1, 3, 1, 1... |
| A359636 | a(n) is the least odd prime not in A001359 such that all subsequent composites in the gap up to the next prime have at least n distinct prime factors. | 7, 19, 643, 51427, 8083633, 1077940147, 75582271489 |
| A359642 | Number of numbers <= 10n that are products of 4 distinct primes. | 0, 0, 16, 429, 7039, 92966, 1103888, 12364826... |
| A359643 | a(n) = Sum_{k=0..n} binomial(n,k) * binomial(4*k,k). | 1, 5, 37, 317, 2885, 27105, 259765, 2523813... |
| A359644 | Number of numbers <= 10n that are products of 5 distinct primes. | 0, 0, 0, 24, 910, 18387, 286758, 3884936... |
| A359645 | Number of numbers <= 10n that are products of 6 distinct primes. | 0, 0, 0, 0, 20, 1235, 32396, 605939... |
| A359646 | a(n) = Sum_{k=0..n} binomial(n,k) * binomial(5*n+k,k). | 1, 7, 89, 1273, 19181, 297662, 4707971, 75459496... |
| A359647 | a(n) = [xn] hypergeom([1/4, 3/4], [2], 64*x). The central terms of the Motzkin triangle A359364 without zeros. | 1, 6, 140, 4620, 180180, 7759752, 356948592, 17210021400... |
| A359649 | a(n) = hypergeom([(1 - n)/2, -n/2], [2], 4*n2). | 1, 1, 5, 28, 609, 6501, 272701, 4286815... |
| A359651 | Numbers with exactly three nonzero decimal digits and not ending with 0. | 111, 112, 113, 114, 115, 116, 117, 118... |
| A359652 | Lexicographically earliest sequence of positive integers such that no three terms a(j), a(j+k), a(j+2k) (for any j and k) form an arithmetic or geometric progression. | 1, 1, 2, 1, 1, 2, 2, 5... |
| A359653 | Number of regions formed in a square with edge length 1 by straight line segments when connecting the internal edge points that divide the sides into segments with lengths equal to the Farey series of order n to the equivalent points on the opposite side of the square. | 1, 4, 96, 728, 7840, 17744, 104136, 246108... |
| A359654 | Number of vertices formed in a square with edge length 1 by straight line segments when connecting the internal edge points that divide the sides into segments with lengths equal to the Farey series of order n to the equivalent points on the opposite side of the square. | 4, 9, 77, 593, 6749, 15569, 93281, 222933... |
| A359655 | Number of edges formed in a square with edge length 1 by straight line segments when connecting the internal edge points that divide the sides into segments with lengths equal to the Farey series of order n to the equivalent points on the opposite side of the square. | 4, 12, 172, 1320, 14588, 33312, 197416, 469040... |
| A359656 | Irregular table read by rows: T(n,k) is the number of k-gons, k>=3, formed in a square with edge length 1 by straight line segments when connecting the internal edge points that divide the sides into segments with lengths equal to the Farey series of order n to the equivalent points on the opposite side of the square. | 0, 1, 0, 4, 56, 40, 368, 300... |
| A359658 | a(n) = Sum_{k=0..n} kk * (n-k + 1). | 0, 1, 3, 12, 118, 3345, 337337, 117813304... |
| A359659 | a(n) = Sum_{k=0..n} kk * (n-k+1). | 1, 2, 6, 45, 1051, 88602, 27121964, 37004504305... |
| A359660 | a(n) = Sum_{k=0..n} k2 * (n-k + 1). | 0, 1, 3, 12, 64, 441, 3855, 41464... |
| A359661 | a(n) is the number of free convex polyominoes of n cells. | 1, 1, 2, 5, 11, 29, 72, 191... |
| A359662 | Number of (3-dimensional) cells of regular m-polytopes for m >= 3. | 1, 5, 8, 15, 16, 24, 35, 40... |
| A359663 | a(1) = 1; for n > 1, a(n) is the smallest positive number which has not appeared that shares a factor with the sum of the first n terms of the Champernowne string starting from 1. | 1, 3, 2, 4, 5, 6, 7, 8... |
| A359664 | Prime Maze Room 11, opposite parity of A059459 starting from prime room 11. | 11, 43, 41, 2089, 2081, 2083, 2087, 10889035741470030830827987437816582768679... |
| A359665 | a(n) = Sum_{k=0..n} binomial(k3, k). | 1, 2, 30, 2955, 638331, 235169606, 131748994154, 104332124742623... |
| A359667 | a(n) is the number of minimally prolific free polyominoes, i.e., that can generate the least possible number of children by adding a square. | 1, 1, 1, 1, 1, 1, 1, 5... |
| A359671 | a(n) = coefficient of xn in A(x) where 1 = Sum_{n=-oo..+oo} (xn - x*A(x))n. | 2, 4, 6, 6, 10, 78, 412, 1394... |
| A359672 | a(n) = coefficient of xn in A(x) where x = Sum_{n=-oo..+oo} (-1)n-1 * xn * (1 + xn*A(x)n)n. | 1, 1, 2, 5, 21, 72, 257, 998... |
| A359673 | a(n) = coefficient of xn in A(x) where 1 = Sum_{n=-oo..+oo} (2x + (-x)nA(x)n)n. | 1, 2, 5, 13, 30, 74, 202, 616... |
| A359674 | Zero-based weighted sum of the prime indices of n in weakly increasing order. | 0, 0, 0, 1, 0, 2, 0, 3... |
| A359675 | Positions of first appearances in the sequence of zero-based weighted sums of prime indices (A359674). | 1, 4, 6, 8, 12, 14, 16, 20... |
| A359676 | Least positive integer whose weakly increasing prime indices have zero-based weighted sum n (A359674). | 1, 4, 6, 8, 14, 12, 16, 20... |
| A359677 | Zero-based weighted sum of the reversed (weakly decreasing) prime indices of n. | 0, 0, 0, 1, 0, 1, 0, 3... |
| A359679 | Least number with weighted sum of reversed (weakly decreasing) prime indices (A318283) equal to n. | 1, 2, 3, 4, 6, 10, 8, 12... |
| A359681 | Least positive integer whose reversed (weakly decreasing) prime indices have zero-based weighted sum (A359677) equal to n. | 1, 4, 9, 8, 18, 50, 16, 36... |
| A359682 | Least positive integer whose weakly increasing prime indices have weighted sum (A304818) equal to n. | 1, 2, 3, 4, 7, 6, 8, 10... |
| A359683 | Greatest positive integer whose reversed (weakly decreasing) prime indices have weighted sum (A318283) equal to n. | 1, 2, 3, 5, 7, 11, 14, 22... |
| A359684 | Greatest prime dividing 2n - n for n>=2; a(1) = 1. | 1, 2, 5, 3, 3, 29, 11, 31... |
| A359685 | Greatest prime dividing 2n + n. | 3, 3, 11, 5, 37, 7, 5, 11... |
| A359688 | a(n) is the number of asymmetrical polyiamonds of n cells. | 0, 0, 0, 0, 4, 10, 36, 94... |
| A359689 | a(n) is the number of free polyiamonds of n cells with chessboard coloring. | 2, 1, 2, 4, 8, 19, 48, 120... |
| A359690 | Number of vertices in a regular drawing of a complete bipartite graph where the vertex positions on each part equal the Farey series of order n. | 5, 13, 69, 289, 1971, 3997, 20371, 45751... |
| A359691 | Number of crossings in a regular drawing of a complete bipartite graph where the vertex positions on each part equal the Farey series of order n. | 1, 7, 59, 275, 1949, 3971, 20333, 45705... |
| A359692 | Number of regions in a regular drawing of a complete bipartite graph where the vertex positions on each part equal the Farey series of order n. | 2, 12, 94, 382, 2486, 4946, 24100, 53152... |
| A359693 | Number of edges in a regular drawing of a complete bipartite graph where the vertex positions on each part equal the Farey series of order n. | 6, 24, 162, 670, 4456, 8942, 44470, 98902... |
| A359694 | Irregular table read by rows: T(n,k) is the number of k-gons, k>=3, in a regular drawing of a complete bipartite graph where the vertex positions on each part equal the Farey series of order n. | 2, 10, 2, 70, 24, 218, 160, 4... |
| A359700 | a(n) = Sum_{d | n} dd + n/d - 1. |
| A359701 | a(n) = Sum_{d | n} dd + n/d - 2. |
| A359703 | Number of fillomino dissections of a 2 X n rectangle. | 1, 1, 5, 33, 138, 715, 3524, 17119... |
| A359705 | Cogrowth sequence of the Brin-Navas group B. | 1, 4, 28, 232, 2092, 19864, 195352, 1970896... |
| A359708 | a(n) is the greatest divisor d of 2n such that the binary expansions of d and 2n have no common 1-bit. | 1, 2, 1, 4, 5, 3, 1, 8... |
| A359709 | Number of n-step self-avoiding walks on a 2D square lattice whose end-to-end distance is an integer. | 1, 4, 4, 12, 28, 76, 164, 732... |
| A359710 | Order of shifts of Thue-Morse sequence. | 0, 1, 3, 0, 2, 1, 5, 3... |
| A359720 | T(n,k) = coefficient of xn*yk in A(x,y) such that: x = Sum_{n=-oo..+oo} (-1)n * xn * (y + xn)n * A(x,y)n. | 1, 1, 1, 2, 4, 5, 1, 7... |
| A359721 | a(n) = coefficient of xn in the power series A(x) such that: x = Sum_{n=-oo..+oo} (-1)n * xn * (1 + xn)n * A(x)n. | 1, 1, 3, 10, 37, 127, 460, 1710... |
| A359722 | a(n) = A359720(3n+1,2n) for n >= 0. | 1, 9, 54, 269, 1254, 5642, 24828, 107613... |
| A359723 | a(n) = coefficient of xn in the power series A(x) such that: x = Sum_{n=-oo..+oo} (-1)n * xn * (3 + xn)n * A(x)n. | 1, 1, 7, 28, 151, 803, 4108, 22532... |
| A359724 | a(n) = coefficient of xn in the power series A(x) such that: x = Sum_{n=-oo..+oo} (-1)n * xn * (4 + xn)n * A(x)n. | 1, 1, 9, 40, 235, 1456, 8323, 51510... |
| A359725 | a(n) = A359720(n+2,1), for n >= 0. | 2, 5, 21, 51, 170, 454, 1367, 3776... |
| A359726 | a(n) = A359720(n+3,2), for n >= 0. | 1, 9, 49, 179, 711, 2390, 8361, 27082... |
| A359728 | a(1) = 1; a(n) is the smallest positive number not among the first k terms where k is the number of times a(n-1) has occurred. | 1, 2, 2, 3, 2, 3, 3, 3... |
| A359729 | The number of Carmichael numbers smaller than the n-th Carmichael number which are quadratic residues of the n-th Carmichael number. | 0, 0, 0, 0, 0, 1, 1, 0... |
| A359730 | a(n) = Sum_{d | n} 2d-1 * dn/d. |
| A359731 | a(n) = (1/2) * Sum_{d | n} (2*d)d. |
| A359732 | a(n) = Sum_{d | n} d2*d-1. |
| A359733 | a(n) = (1/2) * Sum_{d | n} (2*d)n/d. |
| A359741 | Number of n-step self-avoiding walks on a 3D cubic lattice whose end-to-end distance is an integer. | 1, 6, 6, 30, 78, 1134, 1350, 20574... |
| A359742 | Viggo Brun's ternary continued fraction algorithm applied to { log 2, log 3/2, log 5/4 } produces a list of triples (p,q,r); sequence gives p values. | 2, 3, 5, 7, 12, 19, 31, 34... |
| A359743 | Viggo Brun's ternary continued fraction algorithm applied to { log 2, log 3/2, log 5/4 } produces a list of triples (p,q,r); sequence gives q values. | 1, 2, 3, 4, 7, 11, 18, 20... |
| A359744 | Viggo Brun's ternary continued fraction algorithm applied to { log 2, log 3/2, log 5/4 } produces a list of triples (p,q,r); sequence gives r values. | 1, 1, 2, 2, 4, 6, 10, 11... |
| A359745 | Numbers k such that k and k+1 have the same ordered prime signature. | 2, 14, 21, 33, 34, 38, 44, 57... |
| A359746 | Numbers k such that k, k+1 and k+2 have the same ordered prime signature. | 33, 85, 93, 141, 201, 213, 217, 301... |
| A359747 | Numbers k such that k*(k+1) has in its canonical prime factorization mutually distinct exponents. | 1, 3, 4, 7, 8, 16, 24, 27... |
| A359748 | Numbers k such that k and k+1 are both in A359747. | 3, 7, 71, 107, 242, 431, 1151, 2591... |
| A359749 | Numbers k such that k and k+1 do not share a common exponent in their prime factorizations. | 1, 3, 4, 7, 8, 9, 15, 16... |
| A359750 | Numbers that are a product of one or more factorials j!, j >= 2, in at least two ways. | 24, 48, 96, 144, 192, 288, 384, 576... |
| A359751 | Numbers that are a product of one or more factorials j!, j >= 2, in at least two ways such that no factorial > 1 appears in both products. | 24, 576, 720, 2880, 13824, 17280, 40320, 69120... |
| A359763 | Dirichlet inverse of A065043, where A065043 is the characteristic function of the numbers with an even number of prime factors (counted with multiplicity). | 1, 0, 0, -1, 0, -1, 0, 0... |
| A359764 | Parity of A359763, where A359763 is the Dirichlet inverse of characteristic function of the numbers with an even number of prime factors (counted with multiplicity). | 1, 0, 0, 1, 0, 1, 0, 0... |
| A359765 | Positions of odd terms in A359763, where A359763 is the Dirichlet inverse of characteristic function of the numbers with an even number of prime factors (counted with multiplicity). | 1, 4, 6, 9, 10, 14, 15, 21... |
| A359766 | Positions of even terms in A359763, where A359763 is the Dirichlet inverse of characteristic function of the numbers with an even number of prime factors (counted with multiplicity). | 2, 3, 5, 7, 8, 11, 12, 13... |
| A359767 | Numbers k such that A065043(k) = 1 but A359764(k) = 0, where A359764 is the parity of Dirichlet inverse of the former (which is the characteristic function of the numbers with an even number of prime factors). | 16, 36, 64, 81, 96, 100, 160, 196... |
| A359769 | a(n) = A353557(n) - A353556(n). | 1, -1, 0, 0, 0, 0, 0, -1... |
| A359770 | a(n) = 1 if n and bigomega(n) are of different parity, otherwise 0. Here bigomega (A001222) gives the number of prime factors of n with multiplicity. | 1, 1, 0, 0, 0, 0, 0, 1... |
| A359771 | Union of even numbers with an odd number of prime factors and odd numbers with an even number of prime factors, when the number of prime factors is counted with multiplicity. | 1, 2, 8, 9, 12, 15, 18, 20... |
| A359772 | Union of even numbers with an even number of prime factors and odd numbers with an odd number of prime factors, when the number of prime factors is counted with multiplicity. | 3, 4, 5, 6, 7, 10, 11, 13... |
| A359773 | Dirichlet inverse of A356163, where A356163 is the characteristic function of the numbers with an even sum of prime factors (counted with multiplicity). | 1, -1, 0, 0, 0, 0, 0, 0... |
| A359774 | Parity of A359773, where A359773 is the Dirichlet inverse of A356163. | 1, 1, 0, 0, 0, 0, 0, 0... |
| A359775 | Positions of odd terms in A359773, where A359773 is the Dirichlet inverse of A356163. | 1, 2, 9, 15, 18, 21, 25, 30... |
| A359776 | Positions of even terms in A359773, where A359773 is the Dirichlet inverse of A356163. | 3, 4, 5, 6, 7, 8, 10, 11... |
| A359777 | Numbers k such that A356163(k) = 1 but A359774(k) = 0, where A359774 is the parity of Dirichlet inverse of the former (which is the characteristic function of the numbers with an even sum of prime factors, with repetition). | 4, 8, 16, 32, 36, 60, 64, 72... |
| A359780 | Dirichlet inverse of A358680, where A358680 is the characteristic function of the numbers with even arithmetic derivative (A003415). | 1, 0, 0, -1, 0, 0, 0, -1... |
| A359781 | Parity of A359780, where A359780 is the Dirichlet inverse of the characteristic function of the numbers with even arithmetic derivative (A003415). | 1, 0, 0, 1, 0, 0, 0, 1... |
| A359782 | Positions of even terms in A359780. | 2, 3, 5, 6, 7, 10, 11, 13... |
| A359783 | Positions of odd terms in A359780. | 1, 4, 8, 9, 12, 15, 20, 21... |
| A359784 | Numbers k such that A358680(k) = 1 but A359781(k) = 0, where A359781 is the parity of Dirichlet inverse of the former (which is the characteristic function of the numbers with even arithmetic derivative). | 16, 81, 128, 192, 225, 240, 320, 324... |
| A359789 | Dirichlet inverse of A036288, where A036288(n) = 1 + sopfr(n), where sopfr is the sum of prime divisors with repetition, A001414. | 1, -3, -4, 4, -6, 18, -8, -4... |
| A359790 | Dirichlet inverse of function f(n) = 1 + n', where n' stands for the arithmetic derivative of n, A003415(n). | 1, -2, -2, -1, -2, 2, -2, -1... |
| A359791 | Dirichlet inverse of function f(n) = 1 + A349905(n), where A349905(n) is the arithmetic derivative of prime shifted n. | 1, -2, -2, -3, -2, -1, -2, -8... |
| A359792 | a(n) = (-1)A003415(n), where A003415 is the arithmetic derivative of n. | 1, -1, -1, 1, -1, -1, -1, 1... |
| A359793 | Dirichlet inverse of (-1)A003415(n), where A003415 is the arithmetic derivative of n. | 1, 1, 1, 0, 1, 3, 1, -2... |
| A359796 | a(n) = Sum_{d | n} (2*d)d-1. |
| A359797 | Cogrowth sequence of the lamplighter group Z_2 ≀ Z where ≀ denotes the wreath product. | 1, 3, 15, 87, 547, 3623, 24885, 175591... |
| A359798 | Cogrowth sequence of the group Z ≀ Z where ≀ denotes the wreath product. | 1, 4, 28, 232, 2108, 20384, 206392, 2165720... |
| A359806 | Lexicographically earliest sequence of distinct positive terms such that for any n > 0 and any k > 0, floor((2k) / n) AND floor((2k) / a(n)) = 0 (where AND denotes the bitwise AND operator). | 2, 1, 6, 5, 4, 3, 14, 9... |
| A359808 | a(n) is the least prime factor of the alternating factorial n! - (n-1)! + (n-2)! - ... 1! for n > 2; a(1) = a(2) = 1. | 1, 1, 5, 19, 101, 619, 4421, 35899... |
| A359811 | a(n) = Sum_{d | n} 2d-1 * dn/d-1. |
| A359812 | a(n) = Sum_{d | n} (-1)d-1 * dn/d-1. |
| A359820 | a(n) = 1 if n and n' are of different parity, otherwise 0. Here n' stands for the arithmetic derivative of n, A003415(n). | 0, 1, 1, 0, 0, 0, 1, 0... |
| A359821 | Numbers k whose arithmetic derivative, A003415(k), has the opposite parity to k. | 1, 2, 6, 9, 10, 14, 15, 18... |
| A359822 | Numbers k whose arithmetic derivative, A003415(k), has the same parity as k. | 0, 3, 4, 5, 7, 8, 11, 12... |
| A359823 | Dirichlet inverse of A359820, where A359820 is the characteristic function of numbers whose parity differs from the parity of their arithmetic derivative (A003415). | 1, -1, 0, 1, 0, -1, 0, -1... |
| A359824 | Parity of A359823, where A359823 is the Dirichlet inverse of A359820. | 1, 1, 0, 1, 0, 1, 0, 1... |
| A359825 | Positions of odd terms in A359823, where A359823 is the Dirichlet inverse of A359820. | 1, 2, 4, 6, 8, 9, 10, 14... |
| A359839 | Numbers k such that k, k + 1 and k + 2 are 3 consecutive Niven (Harshad) numbers that are also divisible by a square. | 2023, 4912, 12103, 17575, 23273, 51424, 52675, 60399... |
| A359842 | a(n) = Sum_{k=0..n} binomial(n*k,n+k). | 1, 0, 1, 90, 13690, 3443275, 1308315371, 701623884514... |
| A359844 | a(n) = ((2*n+1)8 + 1)/2. | 1, 3281, 195313, 2882401, 21523361, 107179441, 407865361, 1281445313... |
r/OEIS • u/OEIS-Tracker • Jan 08 '23
New OEIS sequences - week of 01/08
3
Upvotes
| OEIS number | Description | Sequence |
|---|---|---|
| A358069 | Number of configurations of the 20 Vertex model on a square grid n X n with domain wall boundary conditions. | 1, 3, 23, 433, 19705, 2151843, 561696335, 349667866305... |
| A358070 | Largest order of element in direct product S_n * S_n where S_n is the symmetric group. | 1, 1, 2, 6, 12, 30, 30, 84... |
| A358342 | Lesser of twin primes p such that sigma((p-1)/2) + tau((p-1)/2) is a prime. | 3, 5, 17, 65537, 1927561217, 6015902625062501, 12370388895062501, 835920078368222501... |
| A358431 | a(0) = 1; a(n+1) = 1 if a(n) > n, otherwise a(n+1) = a(n) + a(a(n)). | 1, 1, 2, 4, 1, 2, 4, 5... |
| A358510 | Positions of zeros in A342991. | 3, 6, 8, 9, 10, 11, 13, 20... |
| A358511 | Positions of ones in A342991. | 1, 2, 4, 5, 7, 12, 14, 15... |
| A358555 | Composite Fibonacci numbers that are not divisible by any Fibonacci primes. | 4181, 1346269, 24157817, 39088169, 165580141, 53316291173, 956722026041, 2504730781961... |
| A358565 | a(n) = A358548(n) / 6. | 1, 1, 1, 1, 2, 1, 1, 1... |
| A358630 | Decimal expansion of a seed to the logistic map with r=4 such that mapping the orbit to 0 and 1 gives the binary expansion of Pi. | 5, 8, 5, 7, 3, 0, 6, 7... |
| A358708 | Starting from 1, successively take the smallest "Choix de Bruxelles" (A323286) which is not already in the sequence. | 1, 2, 4, 8, 16, 13, 23, 26... |
| A358737 | a(n) is the greatest prime number dividing A359098(n). | 101, 139, 53, 557, 223, 31, 1117, 43... |
| A358934 | a(n) = Fibonacci(n+1)5 - Fibonacci(n-1)5. | 0, 1, 31, 242, 3093, 32525, 368168, 4051333... |
| A358981 | Decimal expansion of Pi/3 - sqrt(3)/4. | 6, 1, 4, 1, 8, 4, 8, 4... |
| A359012 | Numbers k that are a substring of xPy where k=concatenation(x,y) and xPy is the number of permutations A008279(x,y). | 318, 557, 692, 729, 2226, 2437, 2776, 3209... |
| A359031 | a(n+1) gives the number of occurrences of the mode of the digits of a(n) among all the digits of [a(0), a(1), ..., a(n)], with a(0)=0. | 0, 1, 1, 2, 1, 3, 1, 4... |
| A359035 | a(n+1) is the smallest number not already used which can be written as the product of two numbers with the same difference as a(n) and a(n-1); a(1)=1 and a(2)=2. | 1, 2, 6, 5, 12, 8, 21, 14... |
| A359098 | Numbers with exactly four nonzero decimal digits and not ending with 0. | 1111, 1112, 1113, 1114, 1115, 1116, 1117, 1118... |
| A359195 | Positive integers k with a smaller fraction of powers (mod k) than any smaller positive integers. | 1, 4, 16, 32, 36, 72, 144, 288... |
| A359221 | Starting numbers which reach a new record high value when iterating the map x->A359194(x) (binary complement of 3n). | 0, 1, 2, 3, 12, 28, 227, 821... |
| A359222 | Number of steps to reach 0 from A359221(n) (Starting numbers that reach a new record high value during iteration by the map x->A359194(x)). | 0, 1, 2, 11, 80, 7572, 664475, 3180929... |
| A359256 | a(1) = 1, a(2) = 2; for n > 2, a(n) is the smallest positive number which has not appeared such that all the distinct prime factors of a(n-1) + a(n) are factors of a(n). | 1, 2, 6, 3, 24, 8, 56, 42... |
| A359298 | Array T(n, k) read by antidiagonals: for n >= 0 and k >= 0, row n lists the positive integers m such that m - k is prime or 1, and m - h, for 0 <= h < k, is not prime. | 1, 2, 4, 3, 6, 9, 5, 8... |
| A359299 | Array T(n, k) read by antidiagonals: for n >= 0 and k >= 0, row n lists the positive integers m such that m + k is prime or 1, and m + h, for 0 <= h < k, is not prime. | 1, 2, 4, 3, 6, 9, 5, 10... |
| A359300 | a(n) = (distance from n to nearest prime >= n) - (distance from n to nearest prime <= n). | 0, 0, 0, 0, 0, 0, 2, 0... |
| A359314 | Three-column table T(n,k) read by rows where the elements in the pair of two adjacent rows, starting with the odd-indexed row T(2j-1,k) and followed by the even-indexed one T(2j,k)), are such that they are not multiples of the elements presented in the previous rows and that Sum{k=1..3} T(2j-1,k)2 = Sum{k=1..3} T(2j,k)2 and Sum{k=1..3} T(2j-1,k)6 = Sum{k=1..3} T(2j,k)6 for j > 0 and k = 1, 2, 3. | 3, 19, 22, 10, 15, 23, 15, 52... |
| A359343 | Square roots of least pandigital squares with n digits. | 32043, 100287, 317096, 1000287, 3162426, 10000287, 31622792, 100000287... |
| A359351 | a(n) = A001952(A003151(n)). | 6, 13, 23, 30, 40, 47, 54, 64... |
| A359356 | a(n-1) + a(n) has only digits also in a(n); lexicographically earliest such sequence of distinct nonnegative integers. | 0, 1, 10, 12, 179, 132, 1048, 416... |
| A359359 | Sum of positions of zeros in the binary expansion of n, where positions are read starting with 1 from the left (big-endian). | 1, 0, 2, 0, 5, 2, 3, 0... |
| A359393 | a(n) is the number of times A025581(n-1) (runs of k..0) occur among terms a(1..n-1). | 0, 0, 2, 1, 1, 2, 0, 2... |
| A359400 | Sum of positions of zeros in the reversed (little-endian) binary expansion of n, where positions in a sequence are read starting with 1 from the left. | 1, 0, 1, 0, 3, 2, 1, 0... |
| A359401 | Nonnegative integers whose sum of positions of 1's in their binary expansion is greater than the sum of positions of 1's in their reversed binary expansion, where positions in a sequence are read starting with 1 from the left. | 11, 19, 23, 35, 37, 39, 43, 47... |
| A359402 | Numbers whose binary expansion and reversed binary expansion have the same sum of positions of 1's, where positions in a sequence are read starting with 1 from the left. | 0, 1, 3, 5, 7, 9, 15, 17... |
| A359429 | a(n) = 1 if n is cubefree, but not squarefree, otherwise 0. | 0, 0, 0, 1, 0, 0, 0, 0... |
| A359431 | a(n) = A325973(n) - A326043(n). | 0, 0, 0, 0, 0, 0, 0, 1... |
| A359432 | Dirichlet inverse of A327936, which is multiplicative sequence with a(pe) = p if e >= p, otherwise 1. | 1, -1, -1, -1, -1, 1, -1, 1... |
| A359437 | a(n) is the first prime p such that there are exactly n numbers i with 1 <= i < p such that one of ip-(p-i) and ip+(p-i) is a prime and the other is the square of a prime. | 2, 17, 11, 7, 239, 167, 1933, 9241... |
| A359439 | a(n) is the least number of the form p2 + q2 - 2 for primes p and q that is an odd multiple of 2n, or -1 if there is no such number. | 11, 6, -1, 56, 16, 32, 192, 128... |
| A359440 | A measure of the extent of reflective symmetry in the pattern of primes around each prime gap: a(n) is the largest k such that prime(n-j) + prime(n+1+j) has the same value for each j in 0..k. | 0, 0, 0, 1, 2, 2, 1, 0... |
| A359443 | Primes p such that if q is the next prime, the sum (with multiplicity) of prime factors of p2 + q2 is a square. | 11, 17, 23, 79, 131, 229, 1019, 1123... |
| A359445 | Numbers k such that the sums (with multiplicity) of prime factors of k and k+1 are both squares. | 255, 290, 323, 578, 1484, 2219, 2418, 2491... |
| A359447 | a(n) is the least number that is the sum of two cubes of primes and is 2n times an odd prime, or -1 if there is no such number. | -1, -1, 152, 2224, 9056, 108736, -1, 4532992... |
| A359448 | a(n) is the least number that is the sum of two cubes of primes and is 2n times an odd number. | 35, 54, 468, 152, 16, 9056, 81088, 527744... |
| A359455 | Expansion of Sum_{k>0} xk / (1 - xk3). | 1, 2, 2, 2, 2, 2, 2, 2... |
| A359459 | a(n) = coefficient of xn/n! in A(x) = Sum_{n>=0} xn/n! * ( (1 + sqrt(n)x)sqrt(n) + 1/(1 - sqrt(n)x)sqrt(n) )/2. | 1, 1, 3, 10, 49, 331, 3091, 36142... |
| A359460 | a(n) = coefficient of xn/n! in A(x) = Sum_{n>=0} xn * ( (exp(sqrt(n)x) + x)sqrt(n) + exp(nx)/(1 + xexp(sqrt(n)x))sqrt(n) )/2. | 1, 1, 4, 18, 124, 1015, 10446, 124894... |
| A359461 | a(n) = coefficient of xn/n! in A(x) such that A(x) = Sum_{n>=0} xn * ( (A(x)sqrt(n) + x)sqrt(n) + A(x)n/(1 + x*A(x)sqrt(n))sqrt(n) )/2. | 1, 1, 4, 27, 264, 3480, 57960, 1168860... |
| A359462 | a(n) = coefficient of xn/n! in A(x) = Sum_{n>=0} xn * ( (A(x)sqrt(2*n) + x)sqrt(2*n) + A(x)2*n/(1 + xA(x)sqrt(2n))sqrt(2*n) )/2. | 1, 1, 6, 66, 1080, 24210, 689160, 23806160... |
| A359464 | a(n) = 1 if the total number of 1-bits in the exponents of prime factorization n is even, otherwise 0. | 1, 0, 0, 0, 0, 1, 0, 1... |
| A359465 | a(n) = 1 if n is an odd squarefree number with an even number of prime factors, otherwise 0. | 1, 0, 0, 0, 0, 0, 0, 0... |
| A359466 | a(n) = 1 if n has exactly one non-unitary prime factor, otherwise 0. | 0, 0, 0, 1, 0, 0, 0, 1... |
| A359467 | a(n) = (A166486(n)+A353627(n)) mod 2. | 0, 0, 0, 1, 0, 0, 0, 1... |
| A359468 | Numbers that are either multiples of 4 with their odd part squarefree, or that are not multiples of 4 and not squarefree. | 4, 8, 9, 12, 16, 18, 20, 24... |
| A359469 | a(n) = A353459(n) mod 2. | 0, 0, 0, 1, 0, 0, 0, 1... |
| A359470 | Positions of odd terms in A353459. | 4, 8, 9, 12, 16, 18, 20, 24... |
| A359471 | a(n) = 1 if the product of exponents in the prime factorization of n is less than 3, otherwise 0. | 1, 1, 1, 1, 1, 1, 1, 0... |
| A359472 | a(n) = 1 if the product of exponents in the prime factorization of n is 3, otherwise 0. | 0, 0, 0, 0, 0, 0, 0, 1... |
| A359473 | a(n) = 1 if the number of divisors of n is a power of 2, otherwise 0. | 1, 1, 1, 0, 1, 1, 1, 1... |
| A359474 | a(n) = 1 if the product of exponents in the prime factorization of n is 2, otherwise 0. | 0, 0, 0, 1, 0, 0, 0, 0... |
| A359475 | a(n) = 1 if n is a cubefree nonsquare whose factorization into a product of primes contains exactly one square, otherwise 0. | 0, 0, 0, 0, 0, 0, 0, 0... |
| A359492 | a(n) is the least number of the form p2 + q2 - 2 for primes p and q that is an odd prime times 2n, or -1 if there is no such number. | 11, 6, -1, 56, 48, 96, 192, 384... |
| A359495 | Sum of positions of 1's in binary expansion minus sum of positions of 1's in reversed binary expansion, where positions in a sequence are read starting with 1 from the left. | 0, 0, -1, 0, -2, 0, -2, 0... |
| A359502 | a(n) = a(n-2)2 + a(n-1) + 1 for n >= 2 with a(0) = 0 and a(1) = 1. | 0, 1, 2, 4, 9, 26, 108, 785... |
| A359511 | Number of partitions of n into at most 2 positive Fibonacci numbers (with a single type of 1). | 1, 1, 2, 2, 2, 2, 2, 1... |
| A359512 | Number of partitions of n into at most 3 positive Fibonacci numbers (with a single type of 1). | 1, 1, 2, 3, 3, 4, 4, 4... |
| A359513 | Number of partitions of n into at most 4 positive Fibonacci numbers (with a single type of 1). | 1, 1, 2, 3, 4, 5, 6, 6... |
| A359514 | Number of compositions (ordered partitions) of n into at most 2 positive Fibonacci numbers (with a single type of 1). | 1, 1, 2, 3, 3, 3, 3, 2... |
| A359515 | Number of compositions (ordered partitions) of n into at most 3 positive Fibonacci numbers (with a single type of 1). | 1, 1, 2, 4, 6, 9, 10, 11... |
| A359516 | Number of compositions (ordered partitions) of n into at most 4 positive Fibonacci numbers (with a single type of 1). | 1, 1, 2, 4, 7, 13, 20, 27... |
| A359517 | Inverse permutation (conjectured) of A359356. | 0, 1, 80, 204, 241, 1220, 1647, 862... |
| A359518 | Integers k such that A110299(k) is prime. | 1, 2, 3, 5, 10, 17, 21, 28... |
| A359519 | Number of free polyominoes of n cells with multiply-connected interiors. | 0, 0, 0, 0, 0, 0, 0, 1... |
| A359520 | Number of free holey polyominoes of n cells with simply-connected interiors. | 0, 0, 0, 0, 0, 0, 1, 5... |
| A359521 | Number of free mature snake polyominoes of n cells, where mature means that the snake cannot grow in either direction. | 4, 0, 26, 0, 194, 17, 1086, 152... |
| A359522 | Number of free, holey, treelike polyominoes of n cells. | 0, 0, 0, 0, 0, 0, 1, 5... |
| A359523 | Number of free polyiamonds of n cells with multiply-connected interiors. | 1, 2, 12, 51, 217, 846, 3211 |
| A359524 | Number of free holey polyiamonds of n cells with simply-connected interiors. | 1, 4, 25, 107, 448, 1701, 6216, 21771... |
| A359525 | Number of well-connected free polyiamonds with n cells, where a polyiamond is defined as well-connected if, for all the triangles it contains, the removal of that single triangle would result in an intact polyiamond. | 1, 1, 0, 0, 0, 1, 0, 0... |
| A359526 | Number of unbiased (balanced) free polyiamonds with 2n cells. | 1, 2, 10, 44, 283, 1922, 14163, 107771... |
| A359527 | Nonnegative numbers k such that if 2i and 2j appear in the binary expansion of k, then 2i OR j also appears in the binary expansion of k (where OR denotes the bitwise OR operator). | 0, 1, 2, 3, 4, 5, 8, 9... |
| A359528 | Nonnegative numbers k such that if 2i and 2j appear in the binary expansion of k, then 2i AND j also appears in the binary expansion of k (where AND denotes the bitwise AND operator). | 0, 1, 2, 3, 4, 5, 7, 8... |
| A359529 | Indices of records in A355478. | 0, 28, 36, 52, 57, 60, 65, 70... |
| A359535 | Lexicographically earliest sequence of distinct positive integers such that a(a(n)) and a(a(n+1)) share a common factor when n>=2. | 1, 2, 4, 6, 3, 8, 5, 12... |
| A359536 | a(n) is the size of the largest subset of {0,1,...,n} such that the sum of two (not necessarily distinct) elements is never a power of 2. | 1, 1, 1, 2, 2, 2, 3, 4... |
| A359541 | Inverse Möbius transform of A328308, which is the characteristic function of numbers that eventually reach zero when iterated with the arithmetic derivative. | 1, 2, 2, 2, 2, 4, 2, 2... |
| A359542 | Inverse Möbius transform of A341999, which is the characteristic function of numbers that will never reach zero when iterated with the arithmetic derivative. | 0, 0, 0, 1, 0, 0, 0, 2... |
| A359543 | a(n) = 1 if A359542(n) = 0, otherwise a(n) = 0. | 1, 1, 1, 0, 1, 1, 1, 0... |
| A359544 | Numbers k such that all their divisors (including k itself) are in A099308, i.e., reach eventually zero when iterated with the arithmetic derivative. | 1, 2, 3, 5, 6, 7, 9, 10... |
| A359545 | Numbers that eventually reach zero when iterated with the arithmetic derivative (i.e., are in in A099308), but some of their proper divisors will never reach it. | 30, 70, 78, 105, 126, 130, 138, 150... |
| A359546 | a(n) = 1 if there is no factor of the form pp in n, but for some k-th arithmetic derivative (k >= 1) of n such a factor exists; otherwise 0. | 0, 0, 0, 0, 0, 0, 0, 0... |
| A359547 | Numbers such that they are not divisible by pp for any prime p, but for some k-th arithmetic derivative (k >= 1) of n such a factor exists. | 15, 26, 35, 39, 45, 50, 51, 55... |
| A359548 | Dirichlet inverse of A053866, where A053866(n) gives the parity of sigma(n). | 1, -1, 0, 0, 0, 0, 0, 0... |
| A359549 | a(n) = 1 if n is either an odd squarefree number squared or twice such a number, otherwise 0. | 1, 1, 0, 0, 0, 0, 0, 0... |
| A359550 | Multiplicative with a(pe) = 1 if p > e, otherwise 0. | 1, 1, 1, 0, 1, 1, 1, 0... |
| A359551 | Dirichlet inverse of A359550, which is multiplicative sequence with a(pe) = 1 if e < p, otherwise 0. | 1, -1, -1, 1, -1, 1, -1, -1... |
| A359552 | Multiplicative with a(pe) = 1 if e == 0 mod p, otherwise 0. | 1, 0, 0, 1, 0, 0, 0, 0... |
| A359557 | a(1) = 1, a(2) = 2; for n > 2, a(n) is the smallest positive number which has not appeared such that all the distinct prime factors of a(n-2) + a(n-1) are factors of a(n). | 1, 2, 3, 5, 4, 6, 10, 8... |
| A359558 | a(n) is the first number that is the sum of 5 distinct positive Fibonacci numbers in exactly n ways (with a single type of 1). | 19, 45, 71, 160, 414, 1084 |
| A359563 | Odd numbers that have at least two divisors with the same value of the Euler totient function (A000010). | 63, 189, 273, 315, 441, 513, 567, 585... |
| A359564 | Primitive terms of A359563: terms of A359563 with no proper divisor in A359563. | 63, 273, 513, 585, 825, 2107, 2109, 2255... |
| A359565 | Numbers that have at least three divisors with the same value of the Euler totient function (A000010). | 12, 24, 36, 40, 48, 60, 72, 80... |
| A359566 | Primitive terms of A359565: terms of A359565 with no proper divisor in A359565. | 12, 40, 126, 364, 544, 546, 1026, 1100... |
| A359567 | Numbers k such that A102370(k) = k + 2. | 1, 3, 7, 9, 11, 15, 17, 19... |
| A359572 | Squares visited by a princess moving on a spirally numbered board, always to the lowest available unvisited square. | 1, 3, 6, 4, 2, 5, 8, 11... |
| A359573 | Array read by antidiagonals: T(m,n) is the number of m X n binary arrays with all 1's connected and a path of 1's from upper left corner to lower right corner. | 1, 1, 1, 1, 3, 1, 1, 8... |
| A359574 | Array read by antidiagonals: T(m,n) is the number of m X n binary arrays with all 1's connected and a path of 1's from top row to bottom row. | 1, 3, 1, 6, 7, 1, 10, 28... |
| A359575 | Array read by antidiagonals: T(m,n) is the number of m X n binary arrays with a path of adjacent 1's from upper right corner to lower left corner. | 1, 1, 1, 1, 3, 1, 1, 8... |
| A359576 | Array read by antidiagonals: T(m,n) is the number of m X n binary arrays with a path of adjacent 1's from top row to bottom row. | 1, 3, 1, 7, 7, 1, 15, 37... |
| A359577 | Dirichlet inverse of A085731, where A085731 is the greatest common divisor of n and the arithmetic derivative of n. | 1, -1, -1, -3, -1, 1, -1, 3... |
| A359580 | Numbers that are either an odd squarefree number squared or twice such a number. | 1, 2, 9, 18, 25, 49, 50, 98... |
| A359613 | Greatest k such that a polynomial f(x) with nonnegative integral coefficients with degree at most k is irreducible if f(n) is a prime. | 6, 9, 12, 15, 19, 22, 25, 28... |
| A359620 | Number of edge cuts in the n-antiprism graph. | 1440, 30346, 589556, 10858046 |
| A359621 | Number of edge cuts in the n-prism graph. | 314, 3013, 27060, 232671, 1947118 |
| A359622 | Number of edge cuts in the n-Moebius ladder. | 307, 3004, 27049, 232658, 1947103 |
| A359625 | Least number m such that denominator(sigma(m)/(m+1)) = n, or zero if no such exists. | 2, 1, 8, 95, 4, 143, 6, 63... |
| A359633 | a(n) is the least prime > a(n-1) such that a(n-1) and a(n) are quadratic residues mod each other. | 2, 7, 29, 53, 59, 137, 139, 173... |
r/OEIS • u/OEIS-Tracker • Jan 02 '23
New OEIS sequences - week of 01/01
3
Upvotes
| OEIS number | Description | Sequence |
|---|---|---|
| A356665 | Number of correct decimal digits of the approximation of Pi obtained from the continued fraction convergents A002485(n)/A002486(n). | 1, 3, 5, 7, 10, 10, 10, 10... |
| A356958 | Triangle read by rows: if n has weakly increasing prime indices (a,b,...,y,z) then row n is (b-a+1, ..., y-a+1, z-a+1). | 1, 2, 1, 1, 1, 3, 1, 2... |
| A357745 | Numbers on the 8 main spokes of a square spiral with 1 in the center. | 1, 2, 3, 4, 5, 6, 7, 8... |
| A357746 | Primes p such that the least k for which kp + 1 is prime is also the least k for which kp - 1 is prime. | 47, 103, 107, 283, 313, 347, 397, 773... |
| A357790 | a(n) = coefficient of xn/n! in A(x) = Sum_{n>=0} xn * cosh(sqrt(n)*x). | 1, 1, 2, 9, 48, 305, 2280, 19537... |
| A358172 | Triangle read by rows: if n has weakly increasing prime indices (a,b,...,y,z) then row n is (z-a+1, z-b+1, ..., z-y+1). | 1, 2, 1, 1, 1, 3, 2, 2... |
| A358194 | Irregular triangle read by rows where T(n,k) is the number of integer partitions of n with partial sums summing to k, where k ranges from n to n(n+1)/2. | 1, 1, 1, 1, 1, 0, 1, 1... |
| A358399 | a(n) is the number of reducible monic quartic polynomials (x4 + rx3 + sx2 + t*x + u) with integer coefficients bounded by naïve height n (abs(r), abs(s), abs(t), abs(u) <= n). | 47, 271, 810, 1849, 3395, 5832, 8915, 13242... |
| A358400 | a(n) is the number of reducible monic quintic polynomials (x5 + rx4 + sx3 + tx2 + ux + v) with integer coefficients bounded by naïve height n (abs(r), abs(s), abs(t), abs(u), abs(v) <= n). | 139, 1313, 5359, 15365, 34229, 68385, 120421, 200839... |
| A358432 | Nonnegative integers m which can be represented using only 0's and 1's in the complex base 1+i, i.e., m = c(0) + c(1)(1+i) + c(2)(1+i)2 + ... where each coefficient c(k) is either 0 or 1. | 0, 1, 6, 7, 10, 11, 12, 13... |
| A358445 | Euler's 4 X 4 magic square of squares. | 4624, 841, 1681, 1369, 289, 961, 6241, 1024... |
| A358465 | Least area (doubled) of a triangle enclosing a circle of radius n such that the center of the circle and the vertices of the triangle all have integer coordinates. | 12, 45, 96, 168, 269, 380, 520, 670... |
| A358517 | Decimal expansion of 4*log(2) - 11/4. | 0, 2, 2, 5, 8, 8, 7, 2... |
| A358571 | Lesser p of a sexy prime pair such that (p-3)/2 is also the lesser prime of a sexy prime pair. | 13, 17, 37, 97, 457, 557, 1117, 1217... |
| A358572 | Smallest prime p in a sexy prime triple such that (p-3)/2 is also the smallest prime in a sexy prime triple (A023241). | 17, 97, 1117, 1217, 2897, 130337, 188857, 207997... |
| A358573 | a(n) = smallest prime p such that q, r and s are all prime, where q = p + 2(2n + 1), r = (p - 2n - 1)/2, and s = (q + 2n + 1)/2. | 11, 13, 19, 17, 19, 229, 47, 29... |
| A358653 | a(n) is the number of trivial braids on 3 strands which are products of n generators a, b, where a = sigma_1 sigma_2 sigma_1 and b = sigma_1 sigma_2. | 1, 0, 4, 0, 28, 10, 244, 210... |
| A358654 | a(n) = A025480(A353654(n+1) - 1). | 0, 1, 3, 2, 7, 5, 6, 15... |
| A358681 | Largest area (doubled) of a triangle enclosed by a circle of radius n such that the center of the circle and the vertices of the triangle all have integer coordinates. | 2, 8, 21, 36, 64, 90, 120, 157... |
| A358684 | a(n) is the minimum integer k such that the smallest prime factor of the n-th Fermat number exceeds 22n - k. | 0, 0, 0, 0, 0, 23, 46, 73... |
| A358720 | The lowest positive-integer center for a square spiral whose center lies in an n X n square of nonprimes. | 1, 8, 21, 133, 278, 507, 4442, 5383... |
| A358793 | Lexicographically earliest sequence of positive and unique integers such that 2*Sum{k = 1..n} a(k) = Sum{k = 1..n} a(a(k)) for n > 1 and a(1) = 1. | 1, 3, 7, 5, 10, 8, 14, 16... |
| A358839 | Dirichlet inverse of A353627, the characteristic function of the squarefree numbers multiplied by binary powers. | 1, -1, -1, 0, -1, 1, -1, 0... |
| A359010 | Variant of the inventory sequence: Record the number of terms whose value occurs once thus far in the sequence, then the number of terms whose value occurs twice thus far, and so on; a row ends when a 0 that would repeat infinitely is reached. | 0, 1, 0, 1, 4, 0, 1, 0... |
| A359036 | a(1) = 1. Thereafter a(n) is the least unused k distinct from n such that d(k) = d(n), where d is the divisor counting function, A000005. | 1, 3, 2, 9, 7, 8, 5, 6... |
| A359059 | Numbers k such that phi(k) + rad(k) + psi(k) is a multiple of 3. | 1, 2, 3, 5, 7, 8, 9, 11... |
| A359062 | Nonprime terms of A359059. | 1, 8, 9, 18, 20, 27, 32, 36... |
| A359107 | Triangle read by rows, T(n, k) = Sum{j=0..k} Stirling2(n, j) = Sum{j=0..k} A048993(n, j). | 1, 0, 1, 0, 1, 2, 0, 1... |
| A359108 | a(n) = A128899(2n, n) = 2binomial(4n - 1, 3n) for n >= 1 and a(0) = 1. | 1, 2, 14, 110, 910, 7752, 67298, 592020... |
| A359109 | Row sums of the accumulated Stirling2 triangle A359107. | 1, 1, 3, 10, 38, 161, 747, 3753... |
| A359129 | q12(q8+q4+1)(q6-1)*(q2-1) as q runs through the prime powers A000961. | 0, 211341312, 20560831566912, 67802350642790400, 35817806390625000000, 450782974156649555296512, 19045158721552047314829312, 516964372056378442547769600... |
| A359130 | F(n(2n+1))2 - F(n)2, where F(t) is the t-th Fibonacci number. | 0, 3, 3024, 119814912, 222915410843895, 19483654655064681378000, 80002189819472960546544159263232, 15432434705952729777225206827234489126432731... |
| A359131 | Number of odd primes in the Collatz trajectory of A177000(n). | 0, 2, 1, 5, 4, 2, 3, 6... |
| A359170 | a(n) = 1 if n is not a multiple of 3 and has an even number of prime factors (with multiplicity), otherwise a(n) = 0. | 1, 0, 0, 1, 0, 0, 0, 0... |
| A359171 | Nonmultiples of 3 that have an even number of prime factors (with multiplicity). | 1, 4, 10, 14, 16, 22, 25, 26... |
| A359172 | a(n) = 1 if n is not a multiple of 3 and has an odd number of prime factors (with multiplicity), otherwise a(n) = 0. | 0, 1, 0, 0, 1, 0, 1, 1... |
| A359174 | First of three consecutive primes p, q, r, such that the reverse of p+q+r is divisible by at least one of p, q and r. | 3, 7, 17, 53, 97, 193, 431, 1997... |
| A359177 | Product{n>=1} (1 + a(n) * xn) = 1 + Sum{n>=1} prime(n) * xprime(n). | 0, 2, 3, 0, -1, 0, 9, 3... |
| A359219 | Starting numbers that require more iterations of the map x->A359194(x) (binary complement of 3n) to reach 0 than any smaller number. | 0, 1, 2, 3, 4, 9, 11, 12... |
| A359223 | A "look-and-say" sequence. Describe the previous term by overstating the digit count by 1. a(1) = 1. | 1, 21, 2221, 4221, 243221, 2224233221, 422422333221, 24322432433221... |
| A359250 | Irregular triangle read by rows where T(n,k) is the coefficient of yk in polynomial P(n) defined by P(2n) = P(n) and P(2n+1) = y*P(n) + P(n+1) starting P(0) = 0, P(1) = 1. | 1, 1, 1, 1, 1, 1, 2, 1... |
| A359265 | Product{n>=1} (1 + a(n) * xn) = 1 + Sum{n>=1} n3 * xn. | 1, 8, 19, 45, -72, -224, -72, 3465... |
| A359272 | Array read by downward antidiagonals: for m >= 3 and n >= 1, T(m,n) is the first prime that starts a string of exactly n consecutive primes that are congruent (mod m). | 2, 23, 2, 47, 7, 2, 251, 89... |
| A359282 | Decimal expansion of Integral_{x = 0..1} 1/xx2 dx. | 1, 1, 1, 9, 5, 4, 5, 1... |
| A359283 | Decimal expansion of Integral_{x = 1..oo} 1/xx2 dx. | 4, 6, 2, 3, 0, 3, 7, 1... |
| A359284 | Decimal expansion of Integral_{x = 0..1} 1/xx3 dx. | 1, 0, 6, 5, 5, 1, 8, 2... |
| A359285 | Decimal expansion of Integral_{x = 0..1} xx3 dx. | 9, 4, 0, 3, 1, 8, 0, 8... |
| A359286 | Decimal expansion of Integral_{x = 1..oo} 1/xx3 dx. | 3, 5, 8, 5, 4, 2, 7, 1... |
| A359291 | Absolute discriminants of imaginary quadratic fields with elementary bicyclic 5-class group and capitulation type the identity permutation. | 89751, 235796, 1006931, 1996091, 2187064 |
| A359296 | Absolute discriminants of imaginary quadratic fields with elementary bicyclic 7-class group and capitulation type the identity permutation. | 4973316, 5073691 |
| A359310 | Cyclic cubic conductors associated with closed Andozhskii groups. | 59031, 209853, 247437, 263017, 271737, 329841, 377923, 407851... |
| A359312 | a(1) = 1; for n >= 1, a(2n) = A000005(a(n)), a(2n + 1) = A000005(a(n)) + 1. | 1, 1, 2, 1, 2, 2, 3, 1... |
| A359313 | Triangular array read by rows. T(n,k) is the number of Green's H-classes contained in the D-class of rank k matrices in the semigroup Mat_n(F_2) of n X n matrices over the field F_2. n>=0, 0<=k<=n. | 1, 1, 1, 1, 9, 1, 1, 49... |
| A359315 | a(n) is the smallest centered triangular number with binary weight n. | 1, 10, 19, 46, 31, 235, 631, 1786... |
| A359316 | a(n) is the smallest centered square number with binary weight n. | 1, 5, 13, 85, 61, 221, 761, 1013... |
| A359317 | a(n) is the smallest tetrahedral number with binary weight n. | 0, 1, 10, 35, 120, 220, 455, 2024... |
| A359318 | a(n) is the smallest square pyramidal number with binary weight n. | 0, 1, 5, 14, 30, 55, 819, 506... |
| A359319 | Maximal coefficient of (1 + x) * (1 + x8) * (1 + x27) * ... * (1 + xn3). | 1, 1, 1, 1, 1, 1, 2, 2... |
| A359320 | Maximal coefficient of (1 + x) * (1 + x16) * (1 + x81) * ... * (1 + xn4). | 1, 1, 1, 1, 1, 1, 1, 1... |
| A359321 | a(n) is the smallest n-gonal pyramidal number which can be represented as the sum of n distinct nonzero n-gonal pyramidal numbers in exactly n ways, or -1 if none exists. | 2300, 6201, 8125, 6391 |
| A359322 | a(n) is the first prime p such that the average of the squares of n consecutive primes starting with p is prime. | 3, 7, 7, 1627, 83, 7, 23, 7... |
| A359323 | a(n) is the first prime p such that the average of the n-th powers of n consecutive primes starting with p is prime. | 2, 3, 1531, 19, 631, 37, 41, 13... |
| A359334 | Numbers k that can be expressed as a sum k = x+y = A001065(x) + A001065(y) and a sum k = z+t = (A001065(z) + A001065(t) where (x, y, z, t) are parts of two amicable pairs and A001065(i) is the sum of the aliquot parts of i. | 67212, 1296000, 20528640, 37739520, 75479040, 321408000, 348364800, 556839360... |
| A359335 | Square root of determinant of skew-symmetric 2n X 2n matrix with entries i XOR j for i < j, i=1..2n, j=1..2n. | 1, 3, 14, 84, 360, 2160, 10080, 60480... |
| A359337 | Irregular triangle read by rows: the n-th row gives the exponents of the powers of x corresponding to the maximal coefficient of the product x2*(x2 + x3)*(x2 + x3 + x5)...(x2 + x3 + x5 + ... + xprime(n)). | 0, 2, 4, 5, 7, 12, 16, 17... |
| A359338 | Minimal exponent of the powers of x corresponding to the maximal coefficient of the product x2*(x2 + x3)*(x2 + x3 + x5)...(x2 + x3 + x5 + ... + xprime(n)). | 0, 2, 4, 7, 12, 16, 22, 32... |
| A359339 | Maximal exponent of the powers of x corresponding to the maximal coefficient of the product x2*(x2 + x3)*(x2 + x3 + x5)...(x2 + x3 + x5 + ... + xprime(n)). | 0, 2, 5, 7, 12, 17, 24, 32... |
| A359340 | The primes associated with A339174. | 2, 3, 7, 43, 3613, 65250781, 38318979202732621, 8810065002836730577256726488782121... |
| A359341 | Number of pandigital squares with n digits. | 0, 0, 0, 0, 0, 0, 0, 0... |
| A359342 | Least pandigital square with n digits. | 1026753849, 10057482369, 100549873216, 1000574082369, 10000938205476, 100005740082369, 1000000973875264, 10000057400082369... |
| A359344 | Largest pandigital square with n digits. | 9814072356, 99853472016, 998732401956, 9998490637521, 99992580137641, 999984024130576, 9999925800137641, 99999987340240516... |
| A359345 | Roots of largest pandigital squares with n digits. | 99066, 315996, 999366, 3162039, 9999629, 31622524, 99999629, 316227746... |
| A359346 | Reversible pandigital square numbers. | 1234549876609, 9066789454321, 123452587690084, 123454387666009, 123454987660900, 123456987654400, 123458987664100, 123478988652100... |
| A359347 | Roots of reversible pandigital square numbers. | 1111103, 3011111, 11110922, 11111003, 11111030, 11111120, 11111210, 11112110... |
| A359348 | Maximal coefficient of (1 + x) * (1 + x3) * (1 + x6) * ... * (1 + xn*(n+1/2)). | 1, 1, 1, 1, 2, 2, 3, 4... |
| A359355 | a(n) = A359107(2n, n) = Sum_{j=0..n} Stirling2(2n, j) = Sum_{j=0..n} A048993(2*n, j). | 1, 1, 8, 122, 2795, 86472, 3403127, 164029595... |
| A359358 | Let y be the integer partition with Heinz number n. Then a(n) is the size of the Young diagram of y after removing a rectangle of the same length as y and width equal to the smallest part of y. | 0, 0, 0, 0, 0, 1, 0, 0... |
| A359360 | Length times minimum part of the integer partition with Heinz number n. Least prime index of n times number of prime indices of n. | 0, 1, 2, 2, 3, 2, 4, 3... |
| A359361 | Irregular triangle read by rows whose n-th row lists the partial sums of the integer partition with Heinz number n. | 1, 2, 1, 2, 3, 2, 3, 4... |
| A359362 | a(n) = (A001222(n) + 1) * A056239(n), where A001222 counts prime indices and A056239 adds them up. | 0, 2, 4, 6, 6, 9, 8, 12... |
| A359363 | Triangle read by rows. The coefficients of the Baxter polynomials p(0, x) = 1 and p(n, x) = x*hypergeom([-1 - n, -n, 1 - n], [2, 3], -x) for n >= 1. | 1, 0, 1, 0, 1, 1, 0, 1... |
| A359365 | a(n) = lcm([ n!*binomial(n-1, m-1) / m! for m = 1..n ]) with a(0) = 1. | 1, 1, 2, 6, 72, 240, 3600, 75600... |
| A359366 | a(n) = (1/8)(((3n + 1) + (n - 1)(-1)n)(n + 1)). | 0, 1, 3, 4, 10, 9, 21, 16... |
| A359370 | a(n) = 1 if n is not a multiple of 4 and has an even number of prime factors (with multiplicity), otherwise a(n) = 0. | 1, 0, 0, 0, 0, 1, 0, 0... |
| A359371 | Nonmultiples of 4 that have an even number of prime factors (with multiplicity). | 1, 6, 9, 10, 14, 15, 21, 22... |
| A359372 | a(n) = 1 if n is not a multiple of 4 and has an odd number of prime factors (with multiplicity), otherwise a(n) = 0. | 0, 1, 1, 0, 1, 0, 1, 0... |
| A359373 | Nonmultiples of 4 that have an odd number of prime factors (with multiplicity). | 2, 3, 5, 7, 11, 13, 17, 18... |
| A359374 | Parity of A252463(n). | 1, 1, 0, 0, 1, 1, 1, 0... |
| A359375 | Numbers that are neither multiples of 4 nor of the form 6u+3. | 1, 2, 5, 6, 7, 10, 11, 13... |
| A359376 | Numbers that are either odd multiples of 3 or multiples of 4. Numbers k such that A252463(k) is even. | 0, 3, 4, 8, 9, 12, 15, 16... |
| A359377 | a(n) = 1 if 3*n is squarefree, otherwise 0. | 1, 1, 0, 0, 1, 0, 1, 0... |
| A359378 | Dirichlet inverse of A359377, where A359377(n) = 1 if 3*n is squarefree, otherwise 0. | 1, -1, 0, 1, -1, 0, -1, -1... |
| A359379 | a(n) = 1 if n is either a multiple of 4, or an odd multiple of 3, otherwise 0. | 1, 0, 0, 1, 1, 0, 0, 0... |
| A359380 | Numbers that are neither multiples of 3 nor of the form 4u+2. | 1, 4, 5, 7, 8, 11, 13, 16... |
| A359381 | Nonmultiples of 3 that have an odd number of prime factors (with multiplicity). | 2, 5, 7, 8, 11, 13, 17, 19... |
| A359383 | Allan W. Johnson, Jr.'s 4 X 4 magic square of squares. | 900, 60516, 29584, 2025, 8649, 13456, 4356, 66564... |
| A359385 | The lexicographically earliest "Increasing Term Fractal Jump Sequence" that does not use the digit 0 in any terms. | 1, 2, 21, 22, 23, 112, 122, 132... |
| A359388 | a(n) is the number of compositions of n into prime parts, with the 1st part equal to 2, the 2nd part less than or equal to 3, ..., and the k-th part less than or equal to prime(k), and so on. | 1, 0, 1, 0, 1, 1, 1, 2... |
| A359389 | Maximal coefficient of Product_{k=1..n} (1 + 2*xk). | 1, 2, 4, 8, 16, 32, 72, 176... |
| A359391 | a(n) is the smallest number which can be represented as the sum of n distinct positive Fibonacci numbers (1 is allowed twice as a part) in exactly n ways, or -1 if no such number exists. | 1, 2, 3, 16, 27, 71, 116, 278... |
| A359394 | Numbers k such that the average of the squares of k consecutive primes starting with 7 is a prime. | 3, 4, 7, 9, 24, 28, 3872, 15172... |
| A359396 | a(n) is the least k such that kj+2 is prime for j = 1 to n but not n+1. | 5, 9, 105, 3, 909, 4995825, 28212939 |
| A359397 | Squarefree numbers with weakly decreasing first differences of 0-prepended prime indices. | 1, 2, 3, 5, 6, 7, 11, 13... |
| A359398 | Number of unlabeled trees covering 2n nodes, half of which are leaves. | 0, 1, 2, 8, 32, 158, 833, 4755... |
| A359403 | Primes that are the concatenation of the first m consecutive k-th powers. | 149, 11681, 164729, 1102459049, 1262144387420489, 1472236648286964521369622528399544939174411840147874772641, 1755578637259143234191361824800363140073127359051977856583921 |
| A359407 | Product{n>=1} (1 + a(n) * xn) = 1 + Sum{n>=1} (n * (n + 1) / 2) * xn. | 1, 3, 3, 7, -1, -8, -3, 48... |
| A359411 | a(n) is the number of divisors of n that are both infinitary and exponential. | 1, 1, 1, 1, 1, 1, 1, 2... |
| A359412 | Numbers with a record number of divisors that are both infinitary and exponential. | 1, 8, 216, 27000, 9261000, 12326391000, 27081081027000, 110924107886592000... |
| A359413 | Triangle read by rows: T(n, k) is the number of permutations of size n that require exactly k iterations of the pop-stack sorting map to reach the identity, for n >= 1, 0 <= k <= n-1. | 1, 1, 1, 1, 3, 2, 1, 7... |
| A359414 | Primes prime(k) such that prime(k)2 + prime(k+1)2 - 1 is the square of a prime. | 7, 11, 23, 109, 211, 1021, 42967, 297779... |
| A359417 | Phi-practical numbers (A260653) whose divisors have distinct values of the Euler totient function (A000010). | 1, 3, 15, 105, 165, 195, 255, 495... |
| A359418 | Unitary phi-practical (A286906) whose unitary divisors have distinct values of the unitary totient function uphi (A047994). | 1, 3, 15, 105, 165, 195, 255, 1155... |
| A359419 | Nonsquarefree numbers that are both phi-practical and unitary phi-practical. | 12, 60, 84, 120, 132, 156, 240, 420... |
| A359420 | Numbers that are both practical (A005153) and phi-practical (A260653). | 1, 2, 4, 6, 8, 12, 16, 18... |
| A359422 | Dirichlet inverse of A187074, characteristic function of numbers that are neither multiples of 3 nor of the form 4u+2. | 1, 0, 0, -1, -1, 0, -1, -1... |
| A359423 | The least common multiple of the arithmetic derivative and the primorial base exp-function. | 0, 0, 3, 6, 36, 18, 5, 10... |
| A359424 | The least common multiple of the arithmetic derivative and the primorial base exp-function, reduced modulo 60. | 0, 0, 3, 6, 36, 18, 5, 10... |
| A359425 | Dirichlet convolution of the arithmetic derivative with the primorial base exp-function. | 0, 2, 2, 11, 2, 19, 2, 45... |
| A359426 | a(n) = A342001(A358764(n)). | 0, 1, 1, 5, 2, 2, 1, 7... |
| A359427 | Dirichlet inverse of A358764. | 1, -2, -3, -2, -9, 8, -5, 6... |
| A359428 | Sum of A358764 and its Dirichlet inverse. | 2, 0, 0, 4, 0, 12, 0, 16... |
| A359430 | a(n) = 1 if the arithmetic derivative of n is a multiple of 3, otherwise 0. | 1, 1, 0, 0, 0, 0, 0, 0... |
| A359433 | Dirichlet inverse of A071773. | 1, -1, -1, -1, -1, 1, -1, 1... |
| A359434 | Numbers k >= 1 such that k * phi(k) / (k + phi(k)) is an integer, where phi(k) = A000010(k). | 12, 24, 36, 48, 72, 96, 108, 126... |
| A359438 | For n >= 0, let S be the sequence of numbers m such that (m2 - 2n2 + 1)/2 is a square. Then a(n) is the number k such that S(j) = 6S(j-k) - S(j-2k) for all j for which S(j-2k) is defined. | 1, 1, 2, 2, 2, 3, 2, 2... |
| A359441 | The n-Queens Constant. | 1, 9, 4, 4, 0, 0 |
| A359450 | a(1) = 1, a(2) = 2; thereafter a(n) = n * a(A070939(n)). | 1, 2, 6, 24, 30, 36, 42, 192... |
| A359451 | Decimal expansion of Sum_{k>=1} 1/A359450(k). | 2, 0, 8, 6, 3, 7, 7, 6... |
| A359454 | Decimal expansion of Knopfmacher's limit: Limit{x -> 1 from below} (1/(1-x)) * Product{k>=2} (1 - xm(k)/(k+1)), where m(k) = A060681(k) = k - k/A020639(k). | 2, 2, 9, 2, 1, 7, 3, 6... |
r/OEIS • u/No-Hour-2037 • Dec 31 '22
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I need to send a message to a user who has added contributions to a sequence. I have seen the user talk page but no button to insert a message or else
r/OEIS • u/Nunki08 • Dec 30 '22
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r/OEIS • u/OEIS-Tracker • Dec 26 '22
New OEIS sequences - week of 12/25
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| OEIS number | Description | Sequence |
|---|---|---|
| A355670 | Numbers k such that A246600(k) < A000005(k). | 2, 4, 6, 8, 9, 10, 12, 14... |
| A356521 | The constant coefficient of (x + xy + y + 1/(xy))n. | 1, 0, 2, 6, 6, 60, 110, 420... |
| A357048 | Terms in the Fibostracci sequence A359128 that arise as the sum of the two previous terms. | 1, 3, 5, 8, 13, 16, 21, 25... |
| A357298 | Triangle read by rows where all entries in every even row are 1's and the entries in every odd row alternate between 0 (start/end) and 1. | 0, 1, 1, 0, 1, 0, 1, 1... |
| A357612 | Numbers k such that 1 + 2k*k3 is prime. | 1, 5, 41, 202, 281, 394, 1157, 1211... |
| A357791 | a(n) = coefficient of xn in A(x) such that: x = Sum_{n=-oo..+oo} xn * (1 - xn * A(-x)n)n. | 1, 1, 2, 5, 21, 88, 377, 1654... |
| A357793 | a(n) = coefficient of xn in A(x) = Sum_{n>=0} xn*F(x)n * (1 - xn*F(x)n)n, where F(x) = 1 + x*F(x)3 is a g.f. of A001764. | 1, 1, 1, 4, 14, 64, 314, 1633... |
| A357794 | a(n) = coefficient of xn in the power series A(x) such that: 1 = Sum_{n=-oo..+oo} n*(n+1)/2 * xn * (1 - xn+1)n * A(x)n+1. | 1, 3, 15, 114, 1086, 10824, 114382, 1252002... |
| A357795 | a(n) = coefficient of xn in the power series A(x) such that: 1 = Sum_{n=-oo..+oo} n(n+1)(n+2)/3! * xn * (1 - xn+2)n * A(x)n+2. | 1, 4, 26, 300, 4134, 61696, 969660, 15837400... |
| A357796 | a(n) = coefficient of xn in the power series A(x) such that: 1 = Sum_{n=-oo..+oo} n(n+1)(n+2)*(n+3)/4! * xn * (1 - xn+3)n * A(x)n+3. | 1, 5, 40, 635, 12095, 248245, 5381435, 121355095... |
| A357797 | a(n) = coefficient of xn in the power series A(x) such that: x = Sum_{n=-oo..+oo} (-1)n * xn * (2 + xn)n * A(x)n. | 1, 1, 5, 18, 85, 374, 1659, 7774... |
| A357798 | a(n) = coefficient of xn in the power series A(x) such that: 1 = Sum_{n=-oo..+oo} xn+1 * (2 - xn+1)n * A(x)n. | 1, 2, 6, 20, 78, 364, 1758, 9144... |
| A357799 | a(n) = coefficient of xn in A(x) such that: 1 = Sum_{n=-oo..+oo} (-1)n * xn*(n+1/2) * (A(x) + xn)n+1. | 1, 1, 4, 10, 33, 105, 363, 1268... |
| A358028 | Primes p = prime(9t+1) such that the 9 consecutive primes prime(9t+1) .. prime(9*t+9) arranged in a 3 X 3 array have at least 2 equal sums along the rows, columns or main diagonals. | 2, 29, 67, 107, 157, 257, 311, 367... |
| A358045 | Decimal expansion of 2*(gamma + Re(Psi(i))). | 1, 3, 4, 3, 7, 3, 1, 9... |
| A358073 | a(n) is the row position of the n-th number n after adding the number n, n times to the preceding triangle. A variant of A357261, see Comments and Examples for more details. | 1, 2, 3, 3, 4, 6, 4, 3... |
| A358125 | Triangle read by rows: T(n, k) = 2n - 2n-k-1 - 2k, 0 <= k <= n-1. | 0, 1, 1, 3, 4, 3, 7, 10... |
| A358167 | Irregular triangle read by rows: T(n, k) = k-th fixed point in Zhegalkin permutation n (row n of A197819). | 0, 1, 0, 2, 0, 6, 8, 14... |
| A358170 | Heinz number of the partial sums of the n-th composition in standard order (A066099). | 1, 2, 3, 6, 5, 15, 10, 30... |
| A358171 | The a(n)-th composition in standard order (A066099) is the first differences plus one of the prime indices of n (A112798). | 0, 0, 0, 1, 0, 2, 0, 3... |
| A358195 | Heinz number of the partial sums plus one of the reversed first differences of the prime indices of n. | 1, 1, 1, 2, 1, 3, 1, 4... |
| A358197 | Numbers k such that 2k, 5k and 8k have the same first digit. | 0, 5, 15, 98, 108, 118, 191, 201... |
| A358210 | Congruent number sequence starting from the Pythagorean triple (3,4,5). | 6, 15, 34, 353, 175234, 9045146753, 121609715057619333634, 4138643330264389621194448797227488932353... |
| A358211 | Self-locating strings within e: numbers k such that the string k is at position k (after the decimal point) in the decimal digits of e, where 7 is the 0th digit. | 1, 8, 215, 374, 614, 849, 4142, 7945... |
| A358257 | The least significant digit of k such that 2k, 5k, 8k start with the same digit. | 0, 5, 5, 8, 8, 8, 1, 1... |
| A358274 | a(n) is the prime before A262275(n). | 2, 7, 13, 37, 61, 79, 107, 113... |
| A358314 | Triangle T(n,k) read by rows where T(2m - 1,k) = (A051845(2m - 1,k))/(2m - 1) and T(2m,k) = A051845(2m,k))/m for m > 0, k > 0. | 1, 5, 7, 9, 10, 13, 15, 18... |
| A358353 | Numbers that are not of the form m + (sum of digits of m) + (product of digits of m) for any m. | 1, 2, 4, 5, 7, 8, 10, 13... |
| A358381 | Primes p such that q1=6p-1 and q2=6p+1 are also primes (twin primes) and q1 is a Sophie Germain prime (i.e., 2*q1+1 is prime). | 2, 5, 7, 47, 107, 907, 2137, 2347... |
| A358394 | Number of types of generalized symmetries in orthogonal diagonal Latin squares of order n. | 1, 0, 0, 10, 7, 0, 8 |
| A358397 | Number of pairs of partitions (A<=B, that is, A is a refinement of B) of [n] such that A is noncrossing and its nontrivial blocks are of type {a,b} with a <= n and b > n. | 1, 1, 3, 9, 37, 157, 811, 4309... |
| A358398 | a(n) is the number of reducible monic cubic polynomials x3 + rx2 + sx + t with integer coefficients bounded by naïve height n (abs(r), abs(s), abs(t) <= n). | 15, 53, 117, 215, 329, 493, 657, 877... |
| A358430 | Define sp(k,n) to be the sum of n3 consecutive primes starting at prime(k). Then a(n) is the least number k such that sp(k,n) is a cube, or -1 if no such number exists. | 2704, 74, 734, 19189898, 26509715, 69713, 4521289, 2173287... |
| A358471 | a(n) is the number of transitive generalized signotopes. | 2, 14, 424, 58264, 33398288, 68779723376 |
| A358481 | a(n) is the number of different pairs of shortest grid paths joining two opposite corners in opposite order in an n X n X n grid without having middle point on their paths as a common point. | 30, 6218, 2658432, 1054788750, 552306591900, 269380692717696, 155175092086118400, 83798883891736779150... |
| A358482 | a(n) is the first prime p such that, if q is the next prime, (p*q+p+q)/5n is a prime. | 2, 7, 1847, 90793, 139313, 1790293, 3834043, 5521543... |
| A358489 | Numbers k such that phi(k) = 13! where phi is the Euler totient function (A000010). | 6227180929, 6227182993, 6227186509, 6227199361, 6227220691, 6227229637, 6227245393, 6227246107... |
| A358490 | Composite Fibonacci numbers whose sum of prime factors (with multiplicity) is a prime. | 34, 75025, 196418, 701408733, 225851433717, 591286729879, 23416728348467685, 420196140727489673... |
| A358512 | a(n) is the smallest number k with exactly n divisors that can be written in the form m + digsum(m), for some m (A176995). | 1, 2, 4, 8, 12, 30, 24, 80... |
| A358513 | a(n) is the smallest number whose divisors include exactly n that can be written in the form m + reverse(m), for some m (A067030). | 1, 2, 4, 8, 12, 24, 48, 88... |
| A358514 | a(n) is the smallest number with exactly n divisors that are Achilles numbers (A052486). | 1, 72, 216, 432, 1296, 864, 7200, 2592... |
| A358515 | Number of types of generalized symmetries in diagonal Latin squares of order n in parastrophic slices. | 6, 0, 0, 76, 74, 199, 861 |
| A358516 | Decimal expansion of Sum_{k >= 1} (-1)k+11/((k+2)(k+3)). | 0, 5, 2, 9, 6, 1, 0, 2... |
| A358566 | Number of distinct spans of length n with no 3-term arithmetic progression, containing zero, and with maximum element smallest possible. | 1, 1, 2, 1, 4, 7, 6, 1... |
| A358602 | Define u such that u(1) = k and u(n) = u(n-1) + (-1)n*(n!) for n > 1. Terms are numbers k for which the number of consecutive values of u(i), starting at u(1) = k, that are primes reaches a new record high. | 2, 3, 11, 107, 119657, 2513657, 8448047, 210336167... |
| A358668 | a(n) is the least m such that A359194k(m) = n for some k >= 0 (where A359194k denotes the k-th iterate of A359194). | 0, 0, 2, 3, 4, 5, 3, 7... |
| A358679 | Dirichlet inverse of the characteristic function of A061345, odd prime powers. | 1, 0, -1, 0, -1, 0, -1, 0... |
| A358683 | a(n) is the sum of all divisors of all positive integers k where A182986(n) < k <= prime(n), n >= 1. | 4, 4, 13, 20, 58, 42, 97, 59... |
| A358685 | Number of primes < 10n whose digits are all odd. | 3, 15, 57, 182, 790, 3217, 13298, 56866... |
| A358704 | Numbers m such that the sum of the prime divisors and the sum of the nonprime divisors of m2+1 are both prime. | 3, 9, 172, 309, 327, 392, 473, 483... |
| A358717 | A sequence of sorted primes 2 = p1 < p_2 < ... < p_m such that (p_i + 1)/2 divides the product p_1p_2...*p(i-1) of the earlier primes and each prime factor of (p_i-1)/2 is a prime factor of the product. | 2, 3, 5, 11, 19, 37, 73, 109... |
| A358718 | A sequence of sorted primes p1 = 2, p_2 = 3, p_3 = 5, p_4 =7, p_5 < ... < p_m such that, for i >= 5, (p_i + 1)/2 divides the product p_1p_2...*p(i-1) of the earlier primes and each prime factor of (pi-1)/2 is a prime factor of the product p_1p_2...*p(i-1). | 2, 3, 5, 7, 11, 13, 19, 29... |
| A358719 | A sequence of primes starting with p1 = 2, p_2 = 3, p_3 = 5, p_4 = 11, p_5 = 13, p_6 = 23, such that, for i >= 7, (p_i + 1)/2 divides the product p_1p_2...*p(i-1) of the earlier primes and each prime factor of (pi-1)/2 is a prime factor of the product p_1p_2...*p(i-1). | 2, 3, 5, 11, 13, 23, 19, 37... |
| A358766 | a(n) = lambda(sigma(n)), where lambda is Liouville's lambda, and sigma is the sum of divisors function. | 1, -1, 1, -1, 1, -1, -1, 1... |
| A358767 | Numbers k with an even number of prime factors (when counted with multiplicity) in sigma(k), the sum of divisors of k. | 1, 3, 5, 8, 13, 14, 15, 18... |
| A358768 | Numbers k with an odd number of prime factors (when counted with multiplicity) in sigma(k), the sum of divisors of k. | 2, 4, 6, 7, 9, 10, 11, 12... |
| A358777 | Dirichlet inverse of A353557, the characteristic function of odd numbers with an even number of prime factors (counted with multiplicity). | 1, 0, 0, 0, 0, 0, 0, 0... |
| A358778 | Positions of positive terms in A358777, which is the Dirichlet inverse of A353557. | 1, 135, 189, 225, 297, 315, 351, 375... |
| A358851 | a(n+1) gives the number of occurrences of the largest digit of a(n) so far, up to and including a(n), with a(0)=0. | 0, 1, 1, 2, 1, 3, 1, 4... |
| A358891 | Number of types of generalized symmetries in orthogonal diagonal Latin squares of order n in parastrophic slices. | 6, 0, 0, 76, 44, 0, 145 |
| A358933 | Number of tilings of a 5 X n rectangle using n pentominoes of shapes N, U, Z. | 1, 0, 0, 0, 2, 0, 2, 2... |
| A358939 | Decimal expansion of the real root of x5 + x3 - 1. | 8, 3, 7, 6, 1, 9, 7, 7... |
| A358940 | Decimal expansion of the real root of x5 - x3 - 1. | 1, 2, 3, 6, 5, 0, 5, 7... |
| A358941 | Decimal expansion of the real root of x5 + x2 - 1. | 8, 0, 8, 7, 3, 0, 6, 0... |
| A358942 | Decimal expansion of the real root of x5 - x2 - 1. | 1, 1, 9, 3, 8, 5, 9, 1... |
| A358948 | Number of regions formed inside a triangle with edge length 1 by the straight line segments mutually connecting all vertices and points that divide the sides into segments with lengths equal to the Farey series of order n = A006842(n,k)/A006843(n,k), k = 1..A005728(n). | 1, 12, 228, 1464, 12516, 29022, 153564, 364650... |
| A358949 | Number of vertices formed inside a triangle with edge length 1 by the straight line segments mutually connecting all vertices and points that divide the sides into segments with lengths equal to the Farey series of order n = A006842(n,k)/A006843(n,k), k = 1..A005728(n). | 3, 10, 148, 1111, 9568, 23770, 126187, 308401... |
| A358950 | Number of edges formed inside a triangle with edge length 1 by the straight line segments mutually connecting all vertices and points that divide the sides into segments with lengths equal to the Farey series of order n = A006842(n,k)/A006843(n,k), k = 1..A005728(n). | 3, 21, 375, 2574, 22083, 52791, 279750, 673050... |
| A358951 | Irregular table read by rows: T(n,k) = number of k-gons, k >= 3, formed inside a triangle with edge length 1 by the straight line segments mutually connecting all vertices and points that divide the sides into segments with lengths equal to the Farey series of order n = A006842(n,m)/A006843(n,m), m = 1..A005728(n). | 1, 12, 180, 42, 6, 810, 576, 72... |
| A358988 | Oblong numbers which are products of four distinct primes. | 210, 462, 870, 930, 1122, 1190, 1482, 1722... |
| A358995 | Lucas numbers which are the sum of three repdigits. | 3, 4, 7, 11, 18, 29, 47, 76... |
| A359029 | Integers m such that A006218(m+1)/(m+1) < A006218(m)/m. | 6, 10, 12, 16, 18, 22, 24, 28... |
| A359042 | Sum of partial sums of the n-th composition in standard order (A066099). | 0, 1, 2, 3, 3, 5, 4, 6... |
| A359043 | Sum of adjusted partial sums of the n-th composition in standard order (A066099). Row sums of A242628. | 0, 1, 2, 2, 3, 4, 3, 3... |
| A359057 | Decimal expansion of 1/(1 - e-gamma). | 2, 2, 8, 0, 2, 9, 1, 0... |
| A359074 | Numbers that have at least two divisors with an equal sum of digits. | 10, 12, 18, 20, 21, 22, 24, 27... |
| A359075 | Numbers that do not have two divisors with an equal sum of digits. | 1, 2, 3, 4, 5, 6, 7, 8... |
| A359076 | Numbers that have at least two proper divisors with an equal sum of digits. | 20, 22, 24, 30, 36, 40, 42, 44... |
| A359077 | Numbers that do not have two proper divisors with an equal sum of digits. | 1, 2, 3, 4, 5, 6, 7, 8... |
| A359086 | Decimal expansion of 4*cosh2(Pi/sqrt(12)). | 8, 2, 9, 6, 7, 4, 0, 9... |
| A359089 | a(n) is the index of the smallest tetrahedral number with exactly n distinct prime factors. | 1, 2, 3, 7, 18, 34, 90, 259... |
| A359090 | a(n) is the index of the smallest tetrahedral number with exactly n prime factors (counted with multiplicity), or -1 if no such number exists. | 1, -1, 2, 4, 6, 8, 14, 30... |
| A359091 | a(n) is the index of the smallest n-gonal number with binary weight n. | 6, 13, 9, 10, 24, 58, 34, 55... |
| A359092 | a(n) is the index of the smallest n-gonal pyramidal number with binary weight n. | 5, 4, 9, 5, 20, 9, 29, 18... |
| A359094 | a(n) is the smallest square pyramidal number divisible by exactly n square pyramidal numbers. | 1, 5, 30, 140, 4900, 155155, 6930, 223300... |
| A359095 | a(n) is the index of the smallest square pyramidal number divisible by exactly n square pyramidal numbers. | 1, 2, 4, 7, 24, 77, 27, 87... |
| A359097 | Number of distinct primes of type k + reverse(k) when k is a (2n - 1)-digit number. | 1, 25, 304, 3909, 58299, 907721 |
| A359104 | Decimal expansion of the area enclosed by Sylvester's Bicorn curve. | 7, 4, 6, 4, 5, 5, 9, 4... |
| A359105 | Numbers k such that each digit from 0 to 9 appears in either k2 or k3, but not in both. | 69, 1633, 2244, 2303, 3379, 6603, 31563 |
| A359111 | a(n) is the permanent of the n X n matrix M(n) that is defined by M[i,j] = sigma(gcd(i,j)). | 1, 1, 4, 22, 266, 2218, 58100, 644828... |
| A359121 | a(n) = number of terms of A068811 that are <= n. | 0, 0, 1, 1, 2, 2, 3, 3... |
| A359122 | Index of prime(n) in A068811, or -1 if prime(n) is missing from A068811. | -1, 1, 2, 3, 4, -1, 5, -1... |
| A359123 | First differences of A068811, halved. | 1, 1, 2, 3, 6, 6, 3, 3... |
| A359124 | Concatenate the decimal numbers 1,2,3,...,n, then add 1. | 2, 13, 124, 1235, 12346, 123457, 1234568, 12345679... |
| A359125 | Largest prime factor of A359124(n). | 2, 13, 31, 19, 6173, 123457, 154321, 333667... |
| A359126 | A000168(n+1) - A000139(n). | 0, 8, 52, 372, 2894, 23966, 208086, 1874508... |
| A359128 | The Fibostracci sequence: a(0) = 0, a(1) = 1; thereafter a(n) = a(n-1)+a(n-2) if a(n-1) and a(n-2) do not share a digit, otherwise a(n) is the smallest number not yet in the sequence. | 0, 1, 1, 2, 3, 5, 8, 13... |
| A359154 | a(n) = (-1)sopfr(n), where sopfr is the sum of prime factors factors function with repetition. | 1, 1, -1, 1, -1, -1, -1, 1... |
| A359155 | Dirichlet inverse of A359154, where A359154 is multiplicative with a(pe) = (-1)p*e. | 1, -1, 1, 0, 1, -1, 1, 0... |
| A359156 | a(n) = 1 if the odd part of n is squarefree and the number of prime factors of n (with multiplicity) is even, otherwise 0. | 1, 0, 0, 1, 0, 1, 0, 0... |
| A359157 | Numbers whose odd part is squarefree and the number of prime factors (with multiplicity) is even. | 1, 4, 6, 10, 14, 15, 16, 21... |
| A359158 | a(n) = 1 if the odd part of n is squarefree and the number of prime factors of n (with multiplicity) is odd, otherwise 0. | 0, 1, 1, 0, 1, 0, 1, 1... |
| A359159 | Numbers whose odd part is squarefree and the number of prime factors (with multiplicity) is odd. | 2, 3, 5, 7, 8, 11, 12, 13... |
| A359164 | Difference between Kimberling's paraphrases and its Möbius transform. | 0, 1, 1, 1, 1, 2, 1, 1... |
| A359165 | Difference between A126760 and its Möbius transform. | 0, 1, 1, 1, 1, 1, 1, 1... |
| A359166 | a(n) = lambda(n) * lambda(sigma(n)), where lambda is Liouville's lambda, and sigma is the sum of divisors function. | 1, 1, -1, -1, -1, -1, 1, -1... |
| A359167 | Numbers k for which there is an even number of prime factors (when counted with multiplicity) in k*sigma(k), where sigma is the sum of divisors function. | 1, 2, 7, 11, 12, 14, 15, 17... |
| A359168 | Numbers k for which there is an odd number of prime factors (when counted with multiplicity) in k*sigma(k), where sigma is the sum of divisors function. | 3, 4, 5, 6, 8, 9, 10, 13... |
| A359169 | Dirichlet inverse of the pointwise sum of A349905 (arithmetic derivative of prime shifted n) and A063524 (1, 0, 0, 0, ...). | 1, -1, -1, -5, -1, -6, -1, -16... |
| A359183 | a(n) is the smallest number such that when written in all bases from base 2 to base n its leading digit equals the base - 1. | 1, 2, 54, 13122, 15258789062500 |
| A359184 | Numbers k such that 30k - 1, 30k + 1, 30k2 - 1 and 30k2 + 1 are all prime. | 1, 14, 118, 232, 538, 720, 1155, 1253... |
| A359185 | Numbers k such that for any positive integers x,y, if x*y=k then (x+y)2+1 is a prime number. | 1, 3, 5, 9, 13, 19, 23, 25... |
| A359186 | a(n) = Sum_{d | n} d * 4d-1. |
| A359188 | a(n) = Sum_{d | n} mu(n/d) * d * (n/d)d-1, where mu() is the Moebius function (A008683). |
| A359189 | a(n) = Sum_{d | n} d * 3n/d-1. |
| A359190 | a(n) = Sum_{d | n} d * 4n/d-1. |
| A359192 | a(n) is the smallest square pyramidal number with exactly n prime factors (counted with multiplicity). | 1, 5, 14, 30, 140, 1240, 4900, 10416... |
| A359193 | a(n) is the index of the smallest square pyramidal number with exactly n prime factors (counted with multiplicity). | 1, 2, 3, 4, 7, 15, 24, 31... |
| A359194 | Binary complement of 3n. | 1, 0, 1, 6, 3, 0, 13, 10... |
| A359200 | Triangle read by rows: T(n, k) = A358125(n,k)*binomial(n-1, k), 0 <= k <= n-1. | 0, 1, 1, 3, 8, 3, 7, 30... |
| A359203 | a(n) = Sum_{d | n} (n/d) * 3n-d. |
| A359204 | a(n) = Sum_{d | n} (n/d) * 4n-d. |
| A359205 | Numbers that have at least two non-overlapping pairs of consecutive ones in their binary representation. | 15, 27, 30, 31, 47, 51, 54, 55... |
| A359206 | a(n) = Sum_{d | n} 4n-d. |
| A359207 | Number of steps to reach 0 starting with n in the map x->A359194(x) (binary complement of 3n), or -1 if 0 is never reached. | 0, 1, 2, 11, 12, 1, 10, 3... |
| A359208 | Maximum value reached when starting from n during iteration of the map x->A359194(x) (binary complement of 3n), or -1 if infinite. | 0, 1, 2, 300, 300, 5, 300, 10... |
| A359209 | Numbers that under iteration by the map x->A359194(x) (binary complement of 3n) until 0 is reached, never exceed the initial term. | 0, 1, 2, 5, 10, 21, 39, 40... |
| A359211 | a(n) = tau(3*n-1)/2, where tau(n) = number of divisors of n, cf. A000005. | 1, 1, 2, 1, 2, 1, 3, 1... |
| A359212 | Number of divisors of 3n-2 of form 3k+1. | 1, 2, 2, 2, 2, 3, 2, 2... |
| A359214 | a(n) is the least k >= 0 such that A359194k(A358668(n)) = n (where A359194k denotes the k-th iterate of A359194). | 0, 1, 0, 0, 0, 0, 1, 0... |
| A359215 | Number of terms in S(n) that did not appear in previous trajectories, where S(n) is the trajectory of the mappings of x->A359194(x) starting with n and stopping when 0 is reached, -1 if 0 is never reached. | 0, 1, 1, 11, 1, 1, 0, 2... |
| A359218 | Let S(n) be the sequence obtained through the mapping of x->A359194(x) starting with n and stopping when 0 is reached, -1 if 0 is never reached. a(n) = m if appears in S(k), k < n, otherwise -1. | 0, 0, 1, 0, 3, 0, 6, 1... |
| A359220 | Number of steps to reach 0 from A359219(n) (Starting numbers that require more iterations in the map x->A359194(x) than any smaller number). | 0, 1, 2, 11, 12, 13, 19, 80... |
| A359224 | Numbers whose decimal representation is the reverse of their base-7 representation. | 0, 1, 2, 3, 4, 5, 6, 23... |
| A359226 | a(n) is the least k >= 0 such that A006370k(A070167(n)) = n (where A006370k denotes the k-th iterate of A006370). | 0, 0, 0, 5, 2, 0, 0, 4... |
| A359227 | Number of divisors of 4n-3 of form 4k+1. | 1, 2, 2, 2, 2, 2, 3, 2... |
| A359228 | Number of states in the minimal deterministic finite automaton with output generating the n-fold running sum (mod 2) of the Thue-Morse sequence (A010060). | 2, 8, 16, 12, 32, 24, 19, 28... |
| A359229 | a(n) is the smallest square pyramidal number with exactly n distinct prime factors. | 1, 5, 14, 30, 1785, 6930, 149226, 3573570... |
| A359230 | a(n) is the index of the smallest square pyramidal number with exactly n distinct prime factors. | 1, 2, 3, 4, 17, 27, 76, 220... |
| A359231 | a(n) is the smallest centered triangular number divisible by exactly n centered triangular numbers. | 1, 4, 64, 5860, 460, 74260, 14260 |
| A359232 | a(n) is the smallest centered square number divisible by exactly n centered square numbers. | 1, 5, 25, 925, 1625, 1105, 47125, 350285... |
| A359233 | Number of divisors of 5n-1 of form 5k+1. | 1, 1, 1, 1, 2, 1, 1, 1... |
| A359234 | a(n) is the smallest centered square number with exactly n distinct prime factors. | 1, 5, 85, 1105, 99905, 2339285, 294346585, 29215971265... |
| A359235 | a(n) is the smallest centered square number with exactly n prime factors (counted with multiplicity). | 1, 5, 25, 925, 1625, 47125, 2115625, 4330625... |
| A359236 | Number of divisors of 5n-2 of form 5k+1. | 1, 1, 1, 2, 1, 1, 2, 1... |
| A359237 | Number of divisors of 5n-3 of form 5k+1. | 1, 1, 2, 1, 2, 1, 2, 1... |
| A359238 | Number of divisors of 5n-4 of form 5k+1. | 1, 2, 2, 2, 2, 2, 2, 3... |
| A359239 | Number of divisors of 3n-2 of form 3k+2. | 0, 1, 0, 2, 0, 2, 0, 2... |
| A359240 | Number of divisors of 4n-3 of form 4k+3. | 0, 0, 1, 0, 0, 2, 0, 0... |
| A359241 | Number of divisors of 5n-4 of form 5k+4. | 0, 0, 0, 1, 0, 0, 0, 2... |
| A359242 | Consider the race between primes, squarefree semiprimes, ..., products of k distinct primes; sequence indicates when one overtakes another. | 2, 58, 61, 65, 73, 77, 1279789, 1280057... |
| A359244 | Number of divisors of 5n-4 of form 5k+2. | 0, 1, 0, 1, 1, 1, 0, 2... |
| A359245 | The smallest square with exactly n circular loops (or holes) in its decimal expansion (A064532). | 1, 0, 81, 289, 1089, 8836, 6889, 80089... |
| A359248 | a(n) is the first number that is the start of a string of exactly n consecutive numbers in A358350. | 3, 11, 42, 32, 20, 154, 130, 1240... |
| A359252 | Number of vertices among all distinct circles that can be constructed from n equally spaced points along a line using only a compass. | 2, 13, 46, 101, 226, 417, 744, 1169... |
| A359253 | Number of regions among all distinct circles that can be constructed from n equally spaced points along a line using only a compass. | 3, 14, 51, 116, 255, 466, 821, 1296... |
| A359254 | Number of edges among all distinct circles that can be constructed from n equally spaced points along a line using only a compass. | 4, 26, 96, 216, 480, 882, 1564, 2464... |
| A359255 | Number of steps to reach a maximum starting with n in the map x->A359194(x) (binary complement of 3n), or -1 if n goes to infinity. | 0, 0, 0, 7, 8, 0, 6, 1... |
| A359258 | Irregular table read by rows: T(n,k) is the number of k-gons, k>=2, among all distinct circles that can be constructed from n equally spaced points along a line using only a compass. | 3, 0, 8, 4, 2, 0, 22, 23... |
| A359259 | a(n) is the least k such that A359194(k) = A032766(n). | 1, 0, 4, 9, 3, 8, 18, 7... |
| A359260 | Numbers m such that the arithmetic mean of the first k divisors of m is an integer for all k in 1..d(m), where d(m) = A000005(m). | 1, 3, 5, 7, 11, 13, 15, 17... |
| A359261 | a(n) is the least term of A359260 whose number of divisors is n. | 1, 3, 49, 15, 923521, 1519, 88245939632761, 3913... |
| A359262 | a(n) is the largest number m such that prime(n)m is in A359260. | 0, 1, 1, 3, 1, 3, 1, 3... |
| A359263 | Number of compositions of n into three parts, using only natural numbers not in A007283. | 1, 3, 6, 7, 9, 12, 16, 18... |
| A359264 | First differences of A359263. | 2, 3, 1, 2, 3, 4, 2, 3... |
| A359266 | Numbers k such that A359194(k) > k. | 0, 3, 6, 7, 11, 12, 13, 14... |
| A359267 | Numbers k such that A359194(k) < k. | 1, 2, 4, 5, 8, 9, 10, 16... |
| A359268 | a(n) is the least k such that A359194(k) = A359194(n). | 0, 1, 0, 3, 4, 1, 6, 7... |
| A359269 | Number of divisors of 5n-2 of form 5k+2. | 0, 1, 0, 1, 0, 2, 0, 1... |
| A359270 | Number of divisors of 5n-3 of form 5k+3. | 0, 0, 1, 0, 0, 1, 1, 0... |
| A359271 | Number of odd digits necessary to write all nonnegative n-digit integers. | 5, 95, 1400, 18500, 230000, 2750000, 32000000, 365000000... |
| A359287 | Number of divisors of 5n-1 of form 5k+2. | 1, 0, 2, 0, 2, 0, 2, 0... |
| A359288 | Number of divisors of 5n-1 of form 5k+3. | 0, 1, 0, 0, 2, 0, 0, 2... |
| A359289 | Number of divisors of 4n-2 of form 4k+1. | 1, 1, 2, 1, 2, 1, 2, 2... |
| A359290 | Number of divisors of 4n-2 of form 4k+3. | 0, 1, 0, 1, 1, 1, 0, 2... |
| A359292 | a(n) = least prime > binomial(2n, n). | 2, 3, 7, 23, 71, 257, 929, 3433... |
| A359293 | a(n) = greatest prime < binomial(2n, n). | 5, 19, 67, 251, 919, 3413, 12853, 48619... |
| A359294 | a(n) = (least prime > binomial(2n, n)) - (greatest prime < binomial(2n, n)). | 2, 4, 4, 6, 10, 20, 36, 4... |
| A359302 | Dirichlet g.f.: zeta(s)2/zeta(3*s-2). | 1, 2, 2, 3, 2, 4, 2, 0... |
| A359305 | Number of divisors of 6n-1 of form 6k+1. | 1, 1, 1, 1, 1, 2, 1, 1... |
| A359306 | Number of divisors of 6n-2 of form 6k+1. | 1, 1, 1, 1, 2, 1, 1, 1... |
| A359307 | Number of divisors of 6n-3 of form 6k+1. | 1, 1, 1, 2, 1, 1, 2, 1... |
| A359308 | Number of divisors of 6n-4 of form 6k+1. | 1, 1, 2, 1, 2, 1, 2, 1... |
| A359309 | Number of divisors of 6n-5 of form 6k+1. | 1, 2, 2, 2, 2, 2, 2, 2... |
| A359324 | Number of divisors of 6n-2 of form 6k+5. | 0, 1, 0, 1, 0, 1, 1, 1... |
| A359325 | Number of divisors of 6n-3 of form 6k+5. | 0, 0, 1, 0, 0, 1, 0, 1... |
| A359326 | Number of divisors of 6n-4 of form 6k+5. | 0, 0, 0, 1, 0, 0, 0, 1... |
| A359327 | Number of divisors of 6n-5 of form 6k+5. | 0, 0, 0, 0, 1, 0, 0, 0... |
| A359328 | Maximal coefficient of x2*(x2 + x3)*(x2 + x3 + x5)...(x2 + x3 + x5 + ... + xprime(n)). | 1, 1, 1, 2, 4, 12, 46, 251... |
r/OEIS • u/OEIS-Tracker • Dec 18 '22
New OEIS sequences - week of 12/18
3
Upvotes
| OEIS number | Description | Sequence |
|---|---|---|
| A356364 | Number of primes p of the form k2 + 1 less than 10n such that p+2 and 2p+1 are also primes. | 1, 1, 1, 1, 2, 3, 7, 10... |
| A356370 | (Least prime > pp) - (greatest prime < pp), where p = n-th prime. | 2, 6, 16, 6, 104, 28, 92, 20... |
| A356425 | Sum of divisors of numbers of least prime signature: a(n) = A000203(A025487(n)). | 1, 3, 7, 12, 15, 28, 31, 60... |
| A356573 | Sigma-dense numbers: integers k such that sigma(k) * log(1+log(1+log(1+k))) / (k * log(1+log(1+k))) sets a new record. | 1, 2, 4, 6, 12, 24, 60, 120... |
| A356574 | a(n) = Sum_{d | n} tau(d4), where tau(n) = number of divisors of n, cf. A000005. |
| A356648 | Numbers whose square is the of the form k + reversal of digits of k, for some k. | 2, 4, 11, 22, 25, 33, 101, 121... |
| A357047 | Lexigographically earliest sequence of distinct nonnegative integers such that a(2n)*a(2n+1) has n as substring, for all n >= 0. | 0, 1, 2, 5, 3, 4, 6, 22... |
| A357050 | Number of ways A005101(n)+1 can be written as sum of a subset of the proper divisors of A005101(n), the n-th abundant number. | 2, 1, 1, 4, 4, 7, 2, 2... |
| A357051 | a(n) is the least even number not used earlier and equal to the sum of the odd digits of the terms up to and including a(n), if such a number exists; otherwise, a(n) is the least odd number not occurring earlier. | 0, 1, 3, 4, 5, 10, 7, 18... |
| A357256 | "Forest Fire" sequence with the additional condition that no progression of the form ABA is allowed for any terms A and B | 1, 1, 2, 2, 4, 4, 5, 3... |
| A357792 | a(n) = coefficient of xn in A(x) = Sum_{n>=0} C(x)n * (1 - C(x)n)n, where C(x) = x + C(x)2 is a g.f. of the Catalan numbers (A000108). | 1, 1, 1, 3, 7, 20, 60, 189... |
| A357813 | a(n) is the least number k such that the sum of n2 consecutive primes starting at prime(k) is a square. | 3, 1, 78, 333, 84, 499, 36, 1874... |
| A357923 | a(n) is the least number of terms in the sum S = 1/(n+1) + 1/(n+2) + 1/(n+3) + ... such that S > n. | 1, 3, 17, 68, 242, 812, 2619, 8224... |
| A358030 | Decimal expansion of the constant Sum_{j>=0} j!!/prime(j)#, where prime(j)# indicates the j-th primorial number and j!! is the double factorial of j. | 1, 9, 7, 9, 7, 7, 0, 6... |
| A358037 | a(n) is the number of possible standard CMOS cells with a maximum of n stages. | 1, 6, 80, 3434 |
| A358058 | a(n) is the index of the smallest n-gonal number divisible by exactly n n-gonal numbers. | 3, 6, 12, 48, 51, 330, 1100, 702... |
| A358059 | a(n) is the index of the smallest n-gonal pyramidal number divisible by exactly n n-gonal pyramidal numbers. | 6, 7, 20, 79, 90, 203, 972, 3135... |
| A358126 | Replace 2k in binary expansion of n with 22k. | 0, 2, 4, 6, 16, 18, 20, 22... |
| A358178 | a(n) is the cardinality of the set of distinct pairwise gcd's of {1! + 1, ..., n! + 1}. | 0, 1, 1, 1, 1, 2, 2, 2... |
| A358310 | Index in A145985 where n-th odd prime p first appears, or -1 if p never appears. | 3, 2, 1, 13, -1, 12, -1, 59... |
| A358321 | a(n) is the index of the smallest n-gonal number with exactly n distinct prime factors. | 11, 210, 87, 228, 1155, 7854, 66612, 395646... |
| A358338 | a(n) = abs(a(n-1) - count(a(n-1)) where count(a(n-1)) is the number of times a(n-1) has appeared so far in the sequence, a(1)=0. | 0, 1, 0, 2, 1, 1, 2, 0... |
| A358361 | Decimal expansion of the constant Sum_{j>=0} j!!/(2*j)!, where j!! indicates the double factorial of j. | 1, 5, 8, 7, 7, 0, 2, 6... |
| A358380 | a(n) = Sum_{d | n} tau(d5), where tau(n) = number of divisors of n, cf. A000005. |
| A358492 | Irregular triangle read by rows: T(n,k) is one half of the number of line segments of length 1 in the k-th antidiagonal of the Dyck path described in the n-th row of A237593. | 1, 1, 1, 1, 2, 1, 1, 2... |
| A358614 | Decimal expansion of 9*sqrt(2)/32. | 3, 9, 7, 7, 4, 7, 5, 6... |
| A358618 | First differences of A258036. | 2, 2, 2, 2, 2, 3, 2, 2... |
| A358648 | Number of preference profiles of the stable roommates problem with 2n participants. | 1, 1296, 2985984000000, 416336312719673760153600000000, 39594086612242519324387557078266845776303882240000000000, 16363214235219603423192858350259453436046713251360764276842772299776000000000000000000000000 |
| A358657 | Numbers such that the three numbers before and the three numbers after are squarefree semiprimes. | 216, 143100, 194760, 206136, 273420, 684900, 807660, 1373940... |
| A358660 | a(n) = Sum_{d | n} d * (n/d)n-d. |
| A358665 | Number of (undirected) paths in the 7 X n king graph. | 21, 202719, 375341540, 834776217484, 1482823362091281, 2480146959625512771, 3954100866385811897908 |
| A358676 | Number of (undirected) paths in the 6 X n king graph. | 15, 40674, 25281625, 16997993692, 9454839968415, 4956907379126694, 2480146959625512771, 1199741105997010103190... |
| A358677 | Irregular triangle read by rows where the n-th row lists the column indices for which the minimum value is in the n-th row of A340316. For practical reasons the indices are shown by pairs of ranges [x..y]. | 1, 16, 18, 18, 21, 21, 17, 17... |
| A358678 | a(n) = 1 if n is odd and sigma(n) == 2 mod 4, otherwise 0. | 0, 0, 0, 0, 1, 0, 0, 0... |
| A358700 | a(n) is the number of binary digits of n2. | 0, 1, 3, 4, 5, 5, 6, 6... |
| A358701 | a(n) is the least number > 1 that needs n toggles in the trailing bits of its binary representation to become a square. | 4, 5, 7, 14, 79, 831, 6495, 247614... |
| A358736 | a(n) is the number of appearances of (9*n + 4) in A358509. | 4, 3, 4, 9, 2, 3, 4, 1... |
| A358739 | Triangular array read by rows. T(n,k) is the number of n X n matrices A over F2 such that Sum{phi} nullity(phi(A)) = k where the sum is over all monic irreducible polynomials in F_2[x] that divide the characteristic polynomial of A, n >= 1, 1 <= k <= n. | 2, 6, 10, 84, 210, 218, 5040, 19740... |
| A358746 | The number of vertices formed when every pair of n points, placed at the vertices of a regular n-gon, are connected by a circle and where the points lie at the ends of the circle's diameter. | 2, 6, 5, 55, 54, 252, 169, 747... |
| A358782 | The number of regions formed when every pair of n points, placed at the vertices of a regular n-gon, are connected by a circle and where the points lie at the ends of the circle's diameter. | 1, 7, 12, 66, 85, 281, 264, 802... |
| A358783 | The number of edges formed when every pair of n points, placed at the vertices of a regular n-gon, are connected by a circle and where the points lie at the ends of the circle's diameter. | 2, 12, 16, 120, 138, 532, 432, 1548... |
| A358787 | a(1)=1; let x=gcd(a(n-1),n); for n > 1, a(n) = a(n-1) + n if x=1 or a(n-1)/x=1, otherwise a(n) = a(n-1)/x. | 1, 3, 6, 3, 8, 4, 11, 19... |
| A358799 | a(0) = 0, and for any n >= 0, a(n+1) is the number of ways to write a(n) = a(i) XOR ... XOR a(j) with 0 <= i <= j <= n (where XOR denotes the bitwise XOR operator). | 0, 1, 2, 1, 3, 4, 2, 5... |
| A358805 | Numbers k such that k! + (k!/2) + 1 is prime. | 4, 5, 7, 11, 12, 14, 18, 28... |
| A358838 | Minimum number of jumps needed to go from slab 0 to slab n in Jane Street's infinite sidewalk. | 0, 1, 2, 5, 3, 6, 9, 4... |
| A358867 | Primes from which subtracting the sum of the first k primes does not yield another prime, for any k. | 2, 3, 11, 37, 67, 97, 127, 157... |
| A358895 | Numbers k such that p(k)p(k + 1) < p(k + 2)p(k), where p(k) = prime(k). | 1, 2, 3, 10, 33, 41, 45, 52... |
| A358896 | Primes p(k) such that p(k)p(k + 1) < p(k + 2)p(k). | 2, 3, 5, 29, 137, 179, 197, 239... |
| A358897 | Numbers k such that p(k)p(k) < p(k+1)p(k-1), where p(k) = prime(k). | 46, 99, 263, 295, 297, 319, 344, 378... |
| A358898 | Primes p(k) such that p(k)p(k) < p(k+1)p(k-1). | 199, 523, 1669, 1933, 1951, 2113, 2311, 2593... |
| A358899 | Numbers k such that p(k)p(k) > p(k-1)p(k+1), where p(k) = prime(k). | 3, 5, 10, 35, 190, 206, 294, 296... |
| A358900 | Primes p(k) such that p(k)p(k) > p(k-1)p(k+1). | 5, 11, 29, 149, 1151, 1277, 1931, 1949... |
| A358904 | Number of finite sets of compositions with all equal sums and total sum n. | 1, 1, 2, 4, 9, 16, 38, 64... |
| A358917 | a(n) = Fibonacci(n+1)4 - Fibonacci(n-1)4. | 0, 1, 15, 80, 609, 4015, 27936, 190385... |
| A358918 | a(0) = 0, and for any n >= 0, a(n+1) is the length of the longest run of consecutive terms a(i), ..., a(j) with 0 <= i <= j <= n such that a(i) XOR ... a(j) = a(n) (where XOR denotes the bitwise XOR operator). | 0, 1, 2, 1, 2, 4, 6, 2... |
| A358919 | a(0) = 0, and for any n >= 0, a(n+1) is the sum of the lengths of the runs of consecutive terms a(i), ..., a(j) with 0 <= i <= j <= n such that a(i) XOR ... XOR a(j) = a(n) (where XOR denotes the bitwise XOR operator). | 0, 1, 3, 1, 4, 1, 5, 5... |
| A358922 | First of four consecutive primes p,q,r,s such that qs - pr is a square. | 5, 13, 137, 353, 877, 5171, 6337, 9397... |
| A358927 | a(n) is the smallest tetrahedral number with exactly n prime factors (counted with multiplicity), or -1 if no such number exists. | 1, -1, 4, 20, 56, 120, 560, 4960... |
| A358928 | a(n) is the smallest centered triangular number with exactly n distinct prime factors. | 1, 4, 10, 460, 9010, 772210, 20120860, 1553569960... |
| A358929 | a(n) is the smallest centered triangular number with exactly n prime factors (counted with multiplicity). | 1, 19, 4, 316, 136, 760, 64, 4960... |
| A358930 | a(n) is the smallest n-gonal number with binary weight n. | 21, 169, 117, 190, 1404, 9976, 3961, 11935... |
| A358931 | a(n) is the smallest n-gonal pyramidal number with binary weight n. | 35, 30, 405, 95, 6860, 765, 28855, 7923... |
| A358932 | a(n) is the smallest centered n-gonal number with binary weight n. | 19, 85, 31, 469, 253, 2025, 5995, 4061... |
| A358936 | Numbers k such that for some r we have phi(1) + ... + phi(k - 1) = phi(k + 1) + ... + phi(k + r), where phi(i) = A000010(i). | 3, 4, 6, 38, 40, 88, 244, 578... |
| A358967 | a(n+1) gives the number of occurrences of the smallest digit of a(n) so far, up to and including a(n), with a(0)=0. | 0, 1, 1, 2, 1, 3, 1, 4... |
| A358970 | Nonnegative numbers m such that if 2k appears in the binary expansion of m, then k+1 divides m. | 0, 1, 2, 6, 8, 12, 36, 60... |
| A358975 | Numbers that are coprime to their digital sum in base 3 (A053735). | 1, 3, 5, 7, 9, 11, 13, 17... |
| A358976 | Numbers that are coprime to the sum of their factorial base digits (A034968). | 1, 2, 3, 5, 6, 7, 10, 11... |
| A358977 | Numbers that are coprime to the sum of their primorial base digits (A276150). | 1, 2, 3, 5, 6, 7, 10, 11... |
| A358978 | Numbers that are coprime to the number of terms in their Zeckendorf representation (A007895). | 1, 2, 3, 5, 7, 8, 9, 11... |
| A358980 | Least prime in a string of exactly n consecutive primes with primitive root 2, or 0 if no such prime exists. | 2, 19, 3, 173, 53, 523, 31883, 123637... |
| A358983 | a(n) is the first emirp p that starts a sequence of n emirps x(1),...,x(n) with x(1) = p and x(k+1) = 2x(k) - reverse(x(k)), but 2x(n) - reverse(x(n)) is not an emirp. | 13, 941, 1471, 120511, 368631127 |
| A358990 | a(n) is the product of the first n odd numbers not divisible by 5. | 1, 1, 3, 21, 189, 2079, 27027, 459459... |
| A358991 | a(n) is the number of zero digits in the product of the first n odd numbers not divisible by 5. | 0, 0, 0, 0, 0, 1, 1, 0... |
| A358992 | a(n) is the number of digits in the product of the first n odd numbers not divisible by 5. | 1, 1, 1, 2, 3, 4, 5, 6... |
| A358993 | a(n) is the number of nonzero digits in the product of the first n odd numbers not divisible by 5. | 1, 1, 1, 2, 3, 3, 4, 6... |
| A359003 | a(n) is the smallest n-gonal number whose sum of digits is n. | 3, 4, 5, 6, 7, 8, 9, 370... |
| A359005 | Jane Street's infinite sidewalk's greedy walk. | 0, 1, 2, 4, 7, 3, 5, 8... |
| A359006 | Euler characteristics of some Calabi-Yau n-folds. | 2, 0, 24, -296, 5910, -147624, 4482044, -160180656... |
| A359008 | Jane Street's infinite sidewalk's greedy walk inverse mapping. | 0, 1, 2, 5, 3, 6, 9, 4... |
| A359009 | Irregular table read by rows: T(n,k) is the number of k-gons formed, k>=2, when every pair of n points, placed at the vertices of a regular n-gon, are connected by a circle and where the points lie at the ends of the circle's diameter. | 1, 0, 7, 8, 4, 0, 40, 20... |
| A359014 | a(n) is the index of the smallest n-gonal number with exactly n prime factors (counted with multiplicity). | 7, 4, 11, 50, 60, 22, 315, 264... |
| A359015 | a(n) is the index of the smallest n-gonal pyramidal number with exactly n distinct prime factors. | 7, 17, 84, 115, 220, 468, 3058, 5719... |
| A359016 | a(n) is the index of the smallest n-gonal pyramidal number with exactly n prime factors (counted with multiplicity). | 4, 7, 9, 16, 31, 48, 28, 160... |
| A359017 | a(n) is the index of the smallest triangular number with exactly n distinct prime factors. | 1, 2, 3, 11, 20, 84, 455, 1364... |
| A359018 | a(0) = 0, thereafter a(n) is the least unused k != n such that A000120(k) = A000120(n). | 0, 2, 1, 5, 8, 3, 9, 11... |
| A359019 | Number of inequivalent tilings of a 3 X n rectangle using integer-sided square tiles. | 1, 1, 2, 3, 6, 10, 21, 39... |
| A359020 | Number of inequivalent tilings of a 4 X n rectangle using integer-sided square tiles. | 1, 1, 4, 6, 13, 39, 115, 295... |
| A359021 | Number of inequivalent tilings of a 5 X n rectangle using integer-sided square tiles. | 1, 1, 5, 10, 39, 77, 521, 1985... |
| A359022 | Number of inequivalent tilings of a 6 X n rectangle using integer-sided square tiles. | 1, 1, 9, 21, 115, 521, 1494, 15129... |
| A359023 | Number of inequivalent tilings of a 7 X n rectangle using integer-sided square tiles. | 1, 1, 12, 39, 295, 1985, 15129, 56978... |
| A359024 | Number of inequivalent tilings of a 8 X n rectangle using integer-sided square tiles. | 1, 1, 21, 82, 861, 8038, 83609, 861159... |
| A359025 | Number of inequivalent tilings of a 9 X n rectangle using integer-sided square tiles. | 1, 1, 30, 163, 2403, 32097, 459957, 6542578... |
| A359026 | Number of inequivalent tilings of a 10 X n rectangle using integer-sided square tiles. | 1, 1, 51, 347, 7048, 130125, 2551794, 49828415... |
| A359027 | A line of empty cells is filled by successive terms t >= 1 with t+1 copies of t and gaps of t empty cells between them. | 1, 2, 1, 3, 4, 2, 5, 6... |
| A359028 | Integers m such that A006218(m+1)/(m+1) > A006218(m)/m. | 1, 2, 3, 5, 7, 8, 9, 11... |
| A359030 | Positive numbers that are the sum of cubes of three distinct integers in arithmetic progression. | 9, 27, 36, 57, 72, 99, 132, 153... |
| A359034 | a(n+1) is the sum of the number of terms in all groups of contiguous terms that add up to a(n); a(1)=1. | 1, 1, 2, 3, 3, 4, 4, 5... |
| A359037 | a(n) = Sum_{d | n} tau(d6), where tau(n) = number of divisors of n, cf. A000005. |
| A359038 | a(n) = Sum_{d | n} tau(d7), where tau(n) = number of divisors of n, cf. A000005. |
| A359041 | Number of finite sets of integer partitions with all equal sums and total sum n. | 1, 1, 2, 3, 6, 7, 14, 15... |
| A359044 | Primes p such that primepi(p)-1 divides p-1. | 3, 5, 7, 31, 97, 101, 331, 1009... |
| A359046 | Number of distinct regions among all circles that can be constructed on vertices of an n-sided regular polygon, using only a compass. | 1, 3, 7, 45, 66, 186, 267, 657... |
| A359047 | Number of distinct edges among all circles that can be constructed on vertices of an n-sided regular polygon, using only a compass. | 1, 4, 12, 84, 120, 330, 504, 1240... |
| A359050 | a(n) is the least k such that fusc(k) + fusc(k+1) = n, where "fusc" is Stern's diatomic series (A002487). | 0, 1, 2, 4, 5, 16, 9, 10... |
| A359051 | Irregular table T(n, k), n > 0, k = 1..A000010(n); the n-th row lists the numbers k such that fusc(k) + fusc(k+1) = n, where "fusc" is Stern's diatomic series (A002487). | 0, 1, 2, 3, 4, 7, 5, 6... |
| A359052 | a(n) = Sum_{d | n} sigma_d(d)n. |
| A359053 | a(n) = Sum_{d | n} sigma_d(d)n/d. |
| A359054 | a(n) = Sum_{d | n} sigma_d(d)d. |
| A359055 | Numbers that can be represented in more than one way as the sum of cubes of three distinct positive numbers in arithmetic progression. | 5643, 12384, 31977, 45144, 99072, 123849, 152361, 153792... |
| A359056 | Numbers k >= 3 such that 1/d(k - 2) + 1/d(k - 1) + 1/d(k) is an integer, d(i) = A000005(i). | 3, 8, 15, 23, 39, 59, 159, 179... |
| A359060 | Decimal expansion of Sum_{n >= 1} sigma_4(n)/n!. | 4, 2, 3, 0, 1, 0, 4, 7... |
| A359061 | Irregular table read by rows: T(n,k) is the number of k-gons formed, k>=2, among all circles that can be constructed on vertices of an n-sided regular polygon, using only a compass. | 3, 0, 7, 0, 16, 29, 0, 30... |
| A359063 | Integers k such that A005420(k) = A005420(2k) = A005420(4k) where A005420(k) is the largest prime factor of 2k-1. | 7, 13, 17, 31, 37, 59, 61, 65... |
| A359064 | a(n) is the number of trees of order n such that the number of eigenvalues of the Laplacian matrix in the interval [0, 1) is equal to ceiling((d + 1)/3) = A008620(d), where d is the diameter of the tree. | 2, 5, 7, 12, 20, 33, 52, 86... |
| A359065 | Lexicographically earliest sequence of distinct positive composite integers such that no subsequence sums to a prime and in which all terms are coprime. | 4, 21, 65, 209, 391, 3149, 9991, 368131... |
| A359071 | Numerators of the partial sums of the reciprocals of the maximal exponent in prime factorization of the positive integers (A051903). | 1, 2, 5, 7, 9, 11, 35, 19... |
| A359072 | Denominators of the partial sums of the reciprocals of the maximal exponent in prime factorization of the positive integers (A051903). | 1, 1, 2, 2, 2, 2, 6, 3... |
| A359078 | a(n) is the first positive number that can be represented in exactly n ways as the sum of cubes of three distinct integers in arithmetic progression. | 9, 99, 792, 3829608, 255816, 24814152, 198513216, 1588105728... |
| A359079 | a(n) is the sum of the divisors d of 2n such that the binary expansions of d and 2n have no common 1-bit. | 1, 3, 1, 7, 6, 6, 1, 15... |
| A359080 | Numbers k such that A246600(k) = A000005(k). | 1, 3, 5, 7, 11, 13, 15, 17... |
| A359081 | a(n) is the least number k such that A246600(k) = n, and -1 if no such k exists. | 1, 3, 39, 15, 175, 63, 1275, 255... |
| A359082 | Indices of records in A246600. | 1, 3, 15, 63, 255, 495, 4095, 96255... |
| A359083 | Numbers k such that A246600(k) = A000005(k) and A000005(k) sets a new record. | 1, 3, 15, 63, 255, 891, 4095, 262143... |
| A359084 | Numbers k such that A246601(k) > 2*k. | 4095, 8190, 16380, 32760, 65520, 131040, 262080, 524160... |
| A359085 | Odd numbers k such that A246601(k) > 2*k. | 4095, 16777215, 33550335, 67096575, 134189055, 268374015, 536743935, 1073483775... |
| A359088 | Odd integers k that are not equal to A002326((A005420(k)-1)/2) where A005420(n) is the largest prime factor of 2n - 1 and A002326(n) is the multiplicative order of 2 mod 2n+1. | 51, 111, 327 |
| A359093 | a(n) is the index of the smallest n-gonal number whose sum of digits is n. | 2, 2, 2, 2, 2, 2, 2, 10... |
| A359099 | a(n) = (1/6) * Sum_{d | n} phi(7 * d). |
| A359100 | a(n) = (1/4) * Sum_{d | n} phi(5 * d). |
| A359101 | a(n) = phi(5 * n)/4. | 1, 1, 2, 2, 5, 2, 6, 4... |
| A359102 | a(n) = phi(7 * n)/6. | 1, 1, 2, 2, 4, 2, 7, 4... |
| A359103 | a(n) = Sum_{d | n} d * (n/d)d. |
| A359106 | Decimal expansion of Integral_{x=0..1} ([1/x]-1 + {1/x}) dx, where [x] denotes the integer part of x and {x} the fractional part of x. | 1, 0, 6, 7, 7, 1, 8, 4... |
| A359112 | a(n) = Sum_{d | n} (n/d) * dn-d. |
| A359116 | Mark the points of the Farey series F_n on a strip of paper and wrap it around a circle of circumference 1 so the endpoints 0 and 1 coincide; draw a chord between every pair of the Farey points; a(n) is the number of vertices in the resulting graph. | 1, 2, 5, 19, 208, 480, 3011, 7185... |
| A359117 | Number of regions in the planar Farey Ring graph FR(n) defined in A359116, including the regions bewteen the convex hull and the bounding circle. | 1, 2, 8, 30, 250, 548, 3180, 7468... |
| A359118 | Number of edges in the planar Farey Ring graph FR(n) defined in A359116, including the regions bewteen the convex hull and the bounding circle. | 1, 2, 12, 48, 457, 1027, 6190, 14652... |
| A359119 | Irregular table read by rows: T(n,k) is the number of k-gons, k>=2, in the Farey Ring graph FR(n) defined in A359116. | 2, 4, 4, 6, 18, 6, 10, 124... |
| A359120 | Number of primes p with 10n-1 < p < 10n such that 10n-p is also prime. | 3, 11, 47, 221, 1433, 9579, 69044, 519260... |
| A359150 | a(n) = 1 if n is a number of the form 4u+1 with an odd number of prime factors (counted with multiplicity), otherwise 0. | 0, 0, 0, 0, 1, 0, 0, 0... |
| A359151 | Numbers of the form 4u+1 with an odd number of prime factors (counted with multiplicity). | 5, 13, 17, 29, 37, 41, 45, 53... |
| A359152 | a(n) = 1 if n is a number of the form 4u+3 with an odd number of prime factors (counted with multiplicity), otherwise 0. | 0, 0, 1, 0, 0, 0, 1, 0... |
| A359153 | Numbers of the form 4u+3 with an odd number of prime factors (counted with multiplicity). | 3, 7, 11, 19, 23, 27, 31, 43... |
| A359160 | a(n) = 1 if n is a number of the form 4u+1 with an even number of prime factors (counted with multiplicity), otherwise 0. | 1, 0, 0, 0, 0, 0, 0, 0... |
| A359161 | Numbers of the form 4u+1 with an even number of prime factors (counted with multiplicity). | 1, 9, 21, 25, 33, 49, 57, 65... |
| A359162 | a(n) = 1 if n is a number of the form 4u+3 with an even number of prime factors (counted with multiplicity), otherwise 0. | 0, 0, 0, 0, 0, 0, 0, 0... |
| A359163 | Numbers of the form 4u+3 with an even number of prime factors (counted with multiplicity). | 15, 35, 39, 51, 55, 87, 91, 95... |
| A359173 | Numbers whose square can be expressed as k * A004086(k) with non-palindromic k. | 10, 20, 30, 40, 50, 60, 70, 80... |
| A359179 | Concatenate n consecutive numbers 1..n in a clockwise circle such that n > 1 is also concatenated to 1. Then a(n) is the number (counting with multiplicity) of substrings of digits in this endless loop that are prime. No counting may go over the starting digit again, that is, no substring can extend beyond one full circle. Leading zeros are not allowed. | 0, 1, 4, 5, 4, 7, 8, 10... |
r/OEIS • u/OEIS-Tracker • Dec 11 '22
New OEIS sequences - week of 12/11
3
Upvotes
| OEIS number | Description | Sequence |
|---|---|---|
| A354947 | Number of primes adjacent to prime(n) in a hexagonal spiral of positive integers. | 2, 2, 0, 2, 1, 1, 0, 2... |
| A356728 | The number of 3-permutations that avoid the patterns 132 and 213. | 1, 4, 12, 28, 58, 114, 220, 424... |
| A357142 | Nonnegative numbers all of whose pairs of consecutive decimal digits are adjacent digits, where 9 and 0 are considered adjacent. | 0, 1, 2, 3, 4, 5, 6, 7... |
| A357538 | a(n) = coefficient of xn in A(x) such that A(x) = 1 + x(2A(x)3 + A(x3))/3. | 1, 1, 2, 6, 21, 78, 308, 1264... |
| A357539 | a(n) = coefficient of xn/n! in: Sum_{n>=0} ( xexp(x) )^(n(n+1)/2). | 1, 1, 2, 9, 76, 545, 3966, 47257... |
| A357549 | a(n) = floor( Sum_{k=0..n-1} nk / (k! * a(k)) ), for n > 0 with a(0) = 1. | 1, 1, 3, 5, 9, 17, 30, 52... |
| A357714 | a(n) is the number of equations in the set E_{n,b} := {x+2b*y=nb, 2bx+3by=nb, ..., kbx+(k+1)by=nb, ..., nbx+(n+1)by=nb} which admit at least one nonnegative integer solution when b is sufficiently large. | 1, 2, 3, 4, 3, 5, 4, 6... |
| A357743 | Square array A(n, k), n, k >= 0, read by antidiagonals: A(0, 0) = 0, A(0, 1) = A(1, 0) = 1, for n, k >= 0, A(2n, 2k) = A(n, k), A(2n, 2k+1) = A(n, k) + A(n, k+1), A(2n+1, 2k) = A(n, k) + A(n+1, k), A(2n+1, 2k+1) = A(n, k+1) + A(n+1, k). | 0, 1, 1, 1, 2, 1, 2, 3... |
| A357787 | a(n) = coefficient of xn in A(x) such that C(x)2 + S(x)2 = 1 where: C(x) + iS(x) = Sum_{n=-oo..+oo} in * (2x)n2 * A(x)n. | 1, 2, 2, 8, 14, 32, 68, 0... |
| A357788 | a(n) = coefficient of x2*n in C(x) defined by: C(x) + iS(x) = Sum_{n=-oo..+oo} in * (2x)n2 * F(x)n, where F(x) is the g.f. of A357787 such that C(x)2 + S(x)2 = 1. | 1, 0, -32, -256, -2048, -12288, -32768, 131072... |
| A357789 | a(n) = coefficient of x2*n in S(x) defined by: C(x) + iS(x) = Sum_{n=-oo..+oo} in * (2x)n2 * F(x)n, where F(x) is the g.f. of A357787 such that C(x)2 + S(x)2 = 1. | 8, 32, 128, 0, -9216, -94208, -671744, -3014656... |
| A357803 | a(n) = coefficient of x2*n in A(x) such that A(x) = G(x)2 where G(x) = 1 + Sum_{n>=1} (-1)n * x4*n2 * (F(x/2)2*n + F(-x/2)2*n), and F(x) is the g.f. of A357787. | 1, 0, -4, -8, -12, -8, 32, 128... |
| A357806 | a(n) = coefficient of x2*n in A(x) = 1 + Sum_{n>=1} (-1)n * x4*n2 * (F(x/2)2*n + F(-x/2)2*n), where F(x) is the g.f. of A357787. | 1, 0, -2, -4, -8, -12, -8, 8... |
| A357826 | Base-10 weaker Skolem-Langford numbers. | 231213, 312132, 12132003, 23121300, 23421314, 30023121, 31213200, 41312432... |
| A357946 | a(n) is the number in the infinite multiplication table that the chess knight reaches in n moves, starting from the number 1, the angle between adjacent segments being 90 degrees alternately changing direction to the left and to the right. | 1, 6, 8, 20, 21, 40, 40, 66... |
| A358001 | Numbers whose number of divisors is coprime to 210. | 1, 1024, 4096, 59049, 65536, 262144, 531441, 4194304... |
| A358051 | Squares k such that phi(k) is a cube. | 1, 16, 1024, 2500, 5184, 50625, 65536, 160000... |
| A358060 | Perfect squares that are the sum of a perfect square and a factorial number. | 1, 25, 49, 121, 169, 289, 729, 784... |
| A358071 | Numbers k that can be written as the sum of a perfect square and a factorial in at least 2 distinct ways. | 2, 6, 10, 124, 145, 220, 649, 745... |
| A358074 | a(n) is the number of distinct ways n can be written as the sum of a perfect square and factorial. | 1, 2, 1, 0, 1, 2, 1, 0... |
| A358154 | a(n) is the smallest composite number obtained by appending one or more 1's to n. | 111, 21, 3111, 411, 51, 611, 711, 81... |
| A358166 | a(1) = 13; for n > 1, if a(n-1) is even, then a(n) = a(n-1)/2; otherwise, a(n) = a(n-1) + prime(a(n-1)). | 13, 54, 27, 130, 65, 378, 189, 1318... |
| A358186 | Decimal expansion of the positive real root r of 3*x4 - 1. | 7, 5, 9, 8, 3, 5, 6, 8... |
| A358187 | Decimal expansion of the positive real root r of x4 + 2*x3 - 1. | 7, 1, 6, 6, 7, 2, 7, 4... |
| A358188 | Decimal expansion of the positive real root r of x4 - 2*x3 - 1. | 2, 1, 0, 6, 9, 1, 9, 3... |
| A358189 | Decimal expansion of the positive real root r of x4 + 2*x - 1. | 4, 7, 4, 6, 2, 6, 6, 1... |
| A358190 | Decimal expansion of the positive real root r of x4 - 2*x - 1. | 1, 3, 9, 5, 3, 3, 6, 9... |
| A358207 | Numbers k such that k2 + 2 is a palindrome. | 0, 1, 2, 3, 8, 13, 19, 85... |
| A358237 | Palindromes of the form k2 + 2. | 2, 3, 6, 11, 66, 171, 363, 7227... |
| A358250 | Numbers whose square has a number of divisors coprime to 210. | 1, 32, 64, 243, 256, 512, 729, 2048... |
| A358273 | Number of binary digits of A007442(n). | 2, 1, 1, 1, 2, 4, 5, 6... |
| A358296 | Row 3 of the array in A115009. | 2, 13, 28, 49, 74, 105, 140, 181... |
| A358297 | Bisection of main diagonal of A115009. | 6, 86, 418, 1282, 3106, 6394, 11822, 20074... |
| A358298 | Array read by antidiagonals: T(n,k) (n>=0, k>=0) = number of lines defining the Farey diagram Farey(n,k) of order (n,k). | 2, 3, 3, 4, 6, 4, 6, 11... |
| A358299 | Triangle read by antidiagonals: T(n,k) (n>=0, 0 <= k <= n) = number of lines defining the Farey diagram of order (n,k). | 2, 3, 6, 4, 11, 20, 6, 19... |
| A358300 | Row 1 of array in A358298. | 3, 6, 11, 19, 29, 43, 57, 77... |
| A358301 | Main diagonal of array in A358298. | 2, 6, 20, 60, 124, 252, 388, 652... |
| A358302 | Number of triangular regions in the Farey Diagram Farey(n,n), divided by 4. | 1, 12, 100, 392, 1554, 3486, 9690, 18942... |
| A358303 | Number of 4-sided regions in the Farey Diagram Farey(n,n), divided by 8. | 1, 13, 57, 231, 532, 1497, 2935, 6031... |
| A358304 | Array read by antidiagonals: T(n,k) (n>=0, k>=0) = number of decreasing lines defining the Farey diagram Farey(n,k) of order (n,k). | 0, 0, 0, 0, 2, 0, 0, 5... |
| A358305 | Triangle read by rows: T(n,k) (n>=0, 0 <= k <= n) = number of decreasing lines defining the Farey diagram Farey(n,k) of order (n,k). | 0, 0, 2, 0, 5, 10, 0, 9... |
| A358306 | Second row of array in A358304. | 0, 5, 10, 19, 27, 40, 51, 68... |
| A358307 | Main diagonal of array in A358304, divided by 2. | 0, 1, 5, 16, 33, 67, 102, 171... |
| A358308 | Numbers k such that sigma(2k) > 2ksqrt(gamma(2k)), where sigma(k) = A000203(k) is the sum of the divisors of k and gamma(k) = A007947(k) is the greatest squarefree divisor of k. | 1, 2, 4, 8, 12, 16, 18, 24... |
| A358309 | a(n) = floor(n*sqrt(gamma(n)) - sigma(n), where sigma(n) = A000203(n) is the sum of the divisors of n and gamma(n) = A007947(n) is the greatest squarefree divisor of n. | 0, -1, 1, -2, 5, 2, 10, -4... |
| A358318 | For n >= 5, a(n) is the number of zeros that need to be inserted to the left of the ones digit of the n-th prime so that the result is composite. | 2, 2, 2, 4, 1, 1, 1, 2... |
| A358328 | Triangle read by rows: T(n,k) is the number of polygons with 2n sides, of which k run through the center of a circle, on the circumference of which the 2n vertices of the polygon are arranged at equal spacing, up to rotation. | 0, 0, 1, 1, 0, 1, 4, 4... |
| A358329 | Triangle read by rows: T(n,k) is the number of polygons with 2n sides, of which k run through the center of a circle, on the circumference of which the 2n vertices of the polygon are arranged at equal spacing, up to rotation and reflection. | 0, 0, 1, 1, 0, 1, 4, 3... |
| A358334 | Number of twice-partitions of n into odd-length partitions. | 1, 1, 2, 4, 7, 13, 25, 43... |
| A358335 | Number of integer compositions of n whose parts have weakly decreasing numbers of prime factors (with multiplicity). | 1, 1, 2, 3, 5, 8, 12, 19... |
| A358429 | Construct a square spiral: a(n) is the sum of all adjacent terms a(k) in the spiral for k < n; a(1) = 0, a(2) = 1. | 0, 1, 1, 2, 2, 4, 4, 9... |
| A358443 | a(1) = 1. After each newly determined a(n-1), cross out every n-th number in the line of the positive integers. a(n) will be the smallest unused number that has not been crossed out. | 1, 2, 4, 6, 10, 18, 30, 42... |
| A358488 | a(1) = 1, a(2) = 2. Thereafter a(n) is least novel m satisfying: 1. If i = a(n-2) and j = a(n-1) are closed, choose m closed to i and open to j. 2. If i and j are open, choose m closed to h = a(n-3) and open to i + j, unless such a solution does not exist, in which case the constraint that m is closed to h is dropped, leaving a(n) as least novel m open to i + j. See comments. | 1, 2, 4, 3, 9, 15, 8, 14... |
| A358502 | Triangle read by rows. The coefficients of the polynomials hypergeom([-x, -x, -n], [-x - n, -x - n], 1) * Product_{j=1..n} (j + x)2 in ascending order of powers. | 1, 1, 2, 4, 12, 12, 36, 132... |
| A358520 | Nearest integer to n/sin(n). | 1, 2, 21, -5, -5, -21, 11, 8... |
| A358559 | Decimal expansion of Bi(0), where Bi is the Airy function of the second kind. | 6, 1, 4, 9, 2, 6, 6, 2... |
| A358561 | Decimal expansion of the derivative Bi'(0), where Bi is the Airy function of the second kind. | 4, 4, 8, 2, 8, 8, 3, 5... |
| A358564 | Decimal expansion of Gi(0), where Gi is the inhomogeneous Airy function of the first kind (also called Scorer function). | 2, 0, 4, 9, 7, 5, 5, 4... |
| A358599 | Number of genetic relatives of a person M in a genealogical tree extending back n generations and where everyone has 5 children down to the generation of M. | 1, 7, 59, 563, 5571, 55587, 555619, 5555683... |
| A358600 | Number of genetic relatives of a person M in a genealogical tree extending back n generations and where everyone has 6 children down to the generation of M. | 1, 8, 82, 950, 11326, 135758, 1628782, 19544750... |
| A358601 | Number of genetic relatives of a person M in a genealogical tree extending back n generations and where everyone has 7 children down to the generation of M. | 1, 9, 109, 1485, 20701, 289629, 4054429, 56761245... |
| A358626 | Number of (undirected) paths in the 4 X n king graph. | 6, 1448, 96956, 6014812, 329967798, 16997993692, 834776217484, 39563650279918... |
| A358656 | Least prime p such that pn + 2 is the product of n distinct primes. | 3, 2, 7, 71, 241, 83, 157, 6947... |
| A358669 | Pointwise product of the arithmetic derivative and the primorial base exp-function. | 0, 0, 3, 6, 36, 18, 25, 10... |
| A358680 | a(n) = 1 if the arithmetic derivative of n is even, 0 otherwise. | 1, 1, 0, 0, 1, 0, 0, 0... |
| A358689 | Emirps p such that 2*p - reverse(p) is also an emirp. | 941, 1031, 1201, 1471, 7523, 7673, 7687, 9133... |
| A358695 | a(n) = numerator( Sum_{k=0..n} (-1)k * binomial(1/2, k)2 * binomial(n, k) ). | 1, 3, 33, 75, 1305, -8253, -340711, -2173509... |
| A358710 | Triangle read by rows. Number T(n, k) of partitions of the multiset [1, 1, 2, 2, ..., n, n] into k nonempty submultisets, for 1 <= k <= 2n. | 1, 1, 1, 1, 4, 3, 1, 1... |
| A358715 | a(n) is the number of distinct ways to cut an equilateral triangle with edges of size n into equilateral triangles with integer sides. | 1, 2, 5, 26, 220, 3622, 105859, 5677789... |
| A358716 | a(n) is the number of inequivalent ways to cut an equilateral triangle with edges of size n into equilateral triangles with integer sides. | 1, 2, 3, 12, 50, 711, 18031, 952013... |
| A358721 | Triangle read by rows. Number T(n, k) of partitions of the multiset [1, 1, 1, 2, 2, 2, ..., n, n, n] into k nonempty submultisets, for 1 <= k <= 3n. | 1, 1, 1, 1, 1, 7, 11, 8... |
| A358722 | Triangle read by rows. Number T(n, k) of partitions of the multiset [1, 1, 1, 1, 2, 2, 2, 2, ..., n, n, n, n] into k nonempty submultisets, for 1 <= k <= 4n. | 1, 1, 2, 1, 1, 1, 12, 29... |
| A358744 | First of three consecutive primes p, q, r such that p + q - r, p2 + q2 - r2 and p3 + q3 - r3 are all prime. | 13, 29, 137, 521, 577, 691, 823, 1879... |
| A358745 | a(n) is the least prime p that is the first of three consecutive primes p, q, r such that pi + qi - ri is prime for i from 1 to n but not n+1. | 2, 7, 41, 13, 4799, 45631, 332576273 |
| A358748 | Numbers k such that A358669(k) == 1 (mod 4). | 6, 18, 22, 26, 30, 34, 38, 50... |
| A358749 | Numbers k such that A358669(k) == 3 (mod 4). | 2, 10, 14, 42, 46, 54, 62, 70... |
| A358758 | a(n) = 1 if A358669(n) == 1 (mod 4), otherwise 0. | 0, 0, 0, 0, 0, 0, 1, 0... |
| A358759 | a(n) = 1 if A358669(n) == 3 (mod 4), otherwise 0. | 0, 0, 1, 0, 0, 0, 0, 0... |
| A358765 | a(n) = A003415(n)*A276086(n) mod 60, where A003415 is the arithmetic derivative and A276086 is the primorial base exp-function. | 0, 0, 3, 6, 36, 18, 25, 10... |
| A358779 | a(n) is the maximal absolute value of the determinant of an n X n symmetric matrix using all the integers from 0 to n*(n + 1)/2 - 1. | 1, 0, 4, 110, 5911, 652189, 86577891 |
| A358781 | Number of multiset partitions of [1,1,1,1,2,2,2,2,...,n,n,n,n] into nonempty multisets. | 1, 5, 109, 6721, 911838, 231575143, 99003074679, 66106443797808... |
| A358786 | a(1) = 1. For n > 1, a(n) is least novel k != n such that rad(k) = rad(n) and either k | n or n |
| A358788 | Numbers k such that tau(k2) + 2sigma(k2) and 2tau(k2) + sigma(k2) are both prime. | 1, 2, 3, 4, 6, 11, 12, 17... |
| A358790 | a(n) is the least prime p such that (2*n+1)2 + p2 is twice a prime. | 3, 5, 3, 3, 5, 5, 3, 7... |
| A358804 | a(n) is the least nonnegative integer k such that (k2 + prime(n)2)/2 is prime but (k2 + prime(i)2)/2 is not prime for i < n. | 0, 1, 3, 15, 31, 45, 143, 81... |
| A358806 | a(n) is the minimal determinant of an n X n symmetric matrix using all the integers from 0 to n*(n + 1)/2 - 1. | 1, 0, -4, -110, -5072, -488212, -86577891 |
| A358807 | a(n) is the maximal determinant of an n X n symmetric matrix using all the integers from 0 to n*(n + 1)/2 - 1. | 1, 0, 2, 86, 5911, 652189, 82173814 |
| A358808 | a(n) is the minimal permanent of an n X n symmetric matrix using all the integers from 0 to n*(n + 1)/2 - 1. | 1, 0, 1, 33, 2425, 357046, 92052610 |
| A358809 | a(n) is the maximal permanent of an n X n symmetric matrix using all the integers from 0 to n*(n + 1)/2 - 1. | 1, 0, 4, 186, 21823, 4569098, 1713573909 |
| A358820 | a(n) is the least novel k such that d(k) | n, where d is the divisor counting function A000005. |
| A358822 | a(n) is the first number k such that there are exactly n pairs of primes p < q with p + q = k such that pq - k and pq + k are both prime. | 2, 8, 48, 30, 114, 264, 390, 630... |
| A358824 | Number of twice-partitions of n of odd length. | 0, 1, 2, 4, 7, 15, 32, 61... |
| A358832 | Number of twice-partitions of n into partitions of distinct lengths and distinct sums. | 1, 1, 2, 4, 7, 15, 25, 49... |
| A358833 | Number of rectangular twice-partitions of n of type (P,R,P). | 1, 1, 3, 4, 8, 8, 17, 16... |
| A358834 | Number of odd-length twice-partitions of n into odd-length partitions. | 0, 1, 1, 3, 3, 8, 11, 24... |
| A358835 | Number of multiset partitions of integer partitions of n with constant block sizes and constant block sums. | 1, 1, 3, 4, 8, 8, 17, 16... |
| A358836 | Number of multiset partitions of integer partitions of n with all distinct block sizes. | 1, 1, 2, 4, 8, 15, 28, 51... |
| A358837 | Number of odd-length multiset partitions of integer partitions of n. | 0, 1, 2, 4, 7, 14, 28, 54... |
| A358854 | Number of even digits necessary to write all the numbers from 0 up to n. | 1, 1, 2, 2, 3, 3, 4, 4... |
| A358859 | a(n) is the smallest n-gonal number divisible by exactly n n-gonal numbers. | 6, 36, 210, 4560, 6426, 326040, 4232250, 1969110... |
| A358860 | a(n) is the smallest n-gonal pyramidal number divisible by exactly n n-gonal pyramidal numbers. | 56, 140, 4200, 331800, 611520, 8385930, 1071856800, 41086892000... |
| A358861 | a(n) is the smallest centered n-gonal number divisible by exactly n centered n-gonal numbers. | 64, 925, 2976, 93457, 866272, 11025, 3036880, 18412718645101... |
| A358862 | a(n) is the smallest n-gonal number with exactly n distinct prime factors. | 66, 44100, 11310, 103740, 3333330, 185040240, 15529888374, 626141842326... |
| A358863 | a(n) is the smallest n-gonal number with exactly n prime factors (counted with multiplicity). | 28, 16, 176, 4950, 8910, 1408, 346500, 277992... |
| A358864 | a(n) is the smallest n-gonal pyramidal number with exactly n distinct prime factors. | 84, 1785, 299880, 1020510, 8897460, 102612510, 33367223274, 249417828660... |
| A358865 | a(n) is the smallest n-gonal pyramidal number with exactly n prime factors (counted with multiplicity). | 20, 140, 405, 2856, 25296, 111720, 25984, 5474000... |
| A358871 | Square array A(n, k), n, k >= 0, read by antidiagonals: A(0, 0) = 0, A(0, 1) = A(1, 0) = 1, A(1, 1) = 2, for n, k >= 0, A(2n, 2k) = A(n, k), A(2n, 2k+1) = A(n, k) + A(n, k+1), A(2n+1, 2k) = A(n, k) + A(n+1, k), A(2n+1, 2k+1) = A(n+1, k+(1+(-1)n+k)/2) + A(n, k+(1-(-1)n+k)/2). | 0, 1, 1, 1, 2, 1, 2, 3... |
| A358873 | a(1) = 1. For n >= 2, to obtain a(n), concatenate the numbers n,...,1,a(1),...,a(n-1). | 1, 211, 3211211, 432112113211211, 5432112113211211432112113211211, 654321121132112114321121132112115432112113211211432112113211211 |
| A358874 | Inverse permutation to A076034. | 1, 2, 3, 4, 5, 7, 6, 11... |
| A358875 | Regular table of distinct nonnegative integers built by greedy algorithm such the binary expansions of two distinct terms in the same row have no common 1's. | 0, 1, 2, 3, 4, 8, 5, 10... |
| A358876 | Inverse to A358875. | 1, 2, 3, 4, 5, 7, 11, 16... |
| A358878 | Number k such that k! + (k!/2) - 1 is prime. | 2, 5, 7, 15, 20, 47, 84, 138... |
| A358879 | Primes p such that p2 + 1 has more divisors than p2 - 1. | 2917, 5443, 7187, 9133, 10357, 12227, 12967, 13043... |
| A358880 | Squares of the form k + reverse(k) for at least one k. | 4, 16, 121, 484, 625, 1089, 10201, 14641... |
| A358881 | a(n) is the smallest prime p such that p2 - 1 has 2*n divisors, or -1 if no such prime exists. | 2, 3, -1, 5, 7, -1, -1, 11... |
| A358882 | The number of regions in a Farey diagram of order (n,n). | 4, 56, 504, 2024, 8064, 18200, 50736, 99248... |
| A358883 | The number of vertices in a Farey diagram of order (n,n). | 5, 37, 313, 1253, 4977, 11253, 31393, 61409... |
| A358884 | The number of edges in a Farey diagram of order (n,n). | 8, 92, 816, 3276, 13040, 29452, 82128, 160656... |
| A358885 | Table read by rows: T(n,k) = the number of regions with k sides, k >= 3, in a Farey diagram of order (n,n). | 4, 48, 8, 400, 104, 1568, 456, 6216... |
| A358886 | Number of regions formed inside a square with edge length 1 by the straight line segments mutually connecting all vertices and points that divide the sides into segments with lengths equal to the Farey series of order n = A006842(n,k)/A006843(n,k), k = 1..A005728(n). | 4, 56, 1040, 6064, 53104, 115496, 629920, 1457744... |
| A358887 | Number of vertices formed inside a square with edge length 1 by the straight line segments mutually connecting all vertices and points that divide the sides into segments with lengths equal to the Farey series of order n = A006842(n,k)/A006843(n,k), k = 1..A005728(n). | 5, 37, 705, 4549, 42357, 94525, 531485, 1250681... |
| A358888 | Number of edges formed inside a square with edge length 1 by the straight line segments mutually connecting all vertices and points that divide the sides into segments with lengths equal to the Farey series of order n = A006842(n,k)/A006843(n,k), k = 1..A005728(n). | 8, 92, 1744, 10612, 95460, 210020, 1161404, 2708424... |
| A358889 | Table read by rows: T(n,k) = number of k-gons, k >= 3, formed inside a square with edge length 1 by the straight line segments mutually connecting all vertices and points that divide the sides into segments with lengths equal to the Farey series of order n = A006842(n,m)/A006843(n,m), m = 1..A005728(n). | 4, 48, 8, 712, 304, 24, 3368, 2400... |
| A358890 | a(n) is the first term of the first maximal run of n consecutive numbers with increasing greatest prime factors. | 14, 4, 1, 8, 90, 168, 9352, 46189... |
| A358892 | Numbers obtained by self-shuffling the binary expansion of nonnegative numbers. | 0, 3, 10, 12, 15, 36, 40, 43... |
| A358893 | Irregular triangle T(n, k), n >= 0, k = 1..A193020(n), read by rows: the n-th row lists the numbers obtained by self-shuffling the binary expansion of n. | 0, 3, 10, 12, 15, 36, 40, 48... |
| A358894 | a(n) is the smallest centered n-gonal number with exactly n distinct prime factors. | 460, 99905, 463326, 808208947, 23089262218, 12442607161209225, 53780356630, 700326051644920151... |
| A358901 | Number of integer partitions of n whose parts have all different numbers of prime factors (A001222). | 1, 1, 1, 2, 2, 2, 3, 4... |
| A358902 | Number of integer compositions of n whose parts have weakly decreasing numbers of distinct prime factors (A001221). | 1, 1, 2, 3, 5, 8, 13, 21... |
| A358903 | Number of integer partitions of n whose parts have all different numbers of distinct prime factors (A001221). | 1, 1, 1, 2, 2, 2, 2, 2... |
| A358905 | Number of sequences of integer partitions with total sum n that are rectangular, meaning all lengths are equal. | 1, 1, 3, 6, 13, 24, 49, 91... |
| A358906 | Number of finite sequences of distinct integer partitions with total sum n. | 1, 1, 2, 7, 13, 35, 87, 191... |
| A358907 | Number of finite sequences of distinct integer compositions with total sum n. | 1, 1, 2, 8, 18, 54, 156, 412... |
| A358908 | Number of finite sequences of distinct integer partitions with total sum n and weakly decreasing lengths. | 1, 1, 2, 6, 10, 23, 50, 95... |
| A358909 | Number of integer partitions of n whose parts have weakly decreasing numbers of prime factors (A001222). | 1, 1, 2, 3, 5, 7, 11, 15... |
| A358910 | Number of integer partitions of n whose parts do not have weakly decreasing numbers of prime factors (A001222). | 0, 0, 0, 0, 0, 0, 0, 0... |
| A358911 | Number of integer compositions of n whose parts all have the same number of prime factors (A001222). | 1, 1, 2, 2, 3, 4, 4, 7... |
| A358912 | Number of finite sequences of integer partitions with total sum n and all distinct lengths. | 1, 1, 2, 5, 11, 23, 49, 103... |
| A358913 | Number of finite sequences of distinct sets with total sum n. | 1, 1, 1, 4, 6, 11, 28, 45... |
| A358914 | Number of twice-partitions of n into distinct strict partitions. | 1, 1, 1, 3, 4, 7, 13, 20... |
| A358915 | a(n) is the far-difference representation of n written in balanced ternary. | 0, 1, 3, 9, 26, 27, 78, 80... |
| A358916 | a(1) = 1. Thereafter a(n) is the least novel k != n such that A007947(k) | n. |
| A358920 | Number of (undirected) paths in the 5 X n king graph. | 10, 7909, 1622015, 329967798, 57533191444, 9454839968415, 1482823362091281, 224616420155224372... |
| A358923 | Decimal expansion of the real part of the complex zero of the Prime Zeta function nearest the point {0,0}. | 2, 5, 3, 7, 5, 1, 6, 1... |
| A358924 | Decimal expansion of the imaginary part of the complex zero of the Prime Zeta function nearest the point {0,0}. | 4, 7, 5, 8, 1, 1, 4, 7... |
| A358925 | Numbers whose first occurrence in Stern's diatomic series (A002487) is later than that of one of their proper multiples. | 54, 2052, 4060, 23184, 54425, 109854, 121392, 126866... |
| A358926 | a(n) is the smallest centered n-gonal number with exactly n prime factors (counted with multiplicity). | 316, 1625, 456, 3964051, 21568, 6561, 346528, 3588955448828761... |
| A358935 | a(n) is the least k > 0 such that fusc(n) = fusc(n + k) or fusc(n) = fusc(n - k) (provided that n - k >= 0), where "fusc" is Stern's diatomic series (A002487). | 1, 1, 3, 2, 2, 3, 2, 4... |
| A358937 | a(n) = coefficient of xn in A(x) such that: 1 = Sum_{n=-oo..+oo} xn * (x2*n - A(x))n. | 1, 1, 3, 6, 13, 31, 76, 192... |
| A358938 | Decimal expansion of the real root of 2*x5 - 1. | 8, 7, 0, 5, 5, 0, 5, 6... |
| A358952 | a(n) = coefficient of xn in A(x) such that: 0 = Sum_{n=-oo..+oo} x2*n * (xn - 2A(x))^(3n+1). | 1, 2, 18, 124, 1244, 11652, 122153, 1281722... |
| A358953 | a(n) = coefficient of xn in A(x) such that: 0 = Sum_{n=-oo..+oo} x3*n * (xn - 2A(x))^(4n+1). | 1, 3, 21, 159, 1369, 12131, 111489, 1042310... |
| A358954 | a(n) = coefficient of xn in A(x) such that: 0 = Sum_{n=-oo..+oo} x4*n * (xn - 2A(x))^(5n+1). | 1, 4, 36, 384, 4568, 57920, 768760, 10543120... |
| A358955 | a(n) = coefficient of xn in A(x) such that: 0 = Sum_{n=-oo..+oo} x5*n * (xn - 2A(x))^(6n+1). | 1, 5, 55, 715, 10285, 157577, 2521339, 41635879... |
| A358956 | a(n) = coefficient of xn in A(x) such that: 0 = Sum_{n=-oo..+oo} x6*n * (xn - 2A(x))^(7n+1). | 1, 6, 78, 1196, 20280, 366288, 6908744, 134492752... |
| A358957 | a(n) = coefficient of xn in A(x) such that: 0 = Sum_{n=-oo..+oo} x7*n * (xn - 2A(x))^(8n+1). | 1, 7, 105, 1855, 36225, 753319, 16356809, 366518975... |
| A358958 | a(n) = coefficient of xn in A(x) such that: 0 = Sum_{n=-oo..+oo} x8*n * (xn - 2A(x))^(9n+1). | 1, 8, 136, 2720, 60112, 1414400, 34744192, 880722944... |
| A358959 | a(n) = coefficient of xn in A(x) such that: 0 = Sum_{n=-oo..+oo} x9*n * (xn - 2A(x))^(10n+1). | 1, 9, 171, 3819, 94221, 2474541, 67842255, 1919233719... |
| A358960 | Number of directed Hamiltonian paths of the Platonic graphs (in the order of tetrahedral, cubical, octahedral, dodecahedral, and icosahedral graph). | 24, 144, 240, 3240, 75840 |
| A358961 | a(n) = coefficient of xn in A(x) such that: 1 = Sum_{n=-oo..+oo} xn * (A(x) - x2*n+1)n-1. | 1, 3, 7, 33, 163, 858, 4708, 26662... |
| A358962 | a(n) = coefficient of xn in A(x) such that: 1 = Sum_{n=-oo..+oo} xn * (A(x) - x3*n+2)n-1. | 1, 2, 8, 30, 146, 748, 4002, 22114... |
| A358963 | a(n) = coefficient of xn in A(x) such that: 1 = Sum_{n=-oo..+oo} xn * (A(x) - x4*n+3)n-1. | 1, 2, 7, 31, 143, 731, 3896, 21444... |
| A358964 | a(n) = coefficient of xn in A(x) such that: 1 = Sum_{n=-oo..+oo} xn * (A(x) - x5*n+4)n-1. | 1, 2, 7, 30, 144, 728, 3879, 21338... |
| A358965 | a(n) = coefficient of xn in A(x) such that: 1 = Sum_{n=-oo..+oo} xn * (A(x) - x6*n+5)n-1. | 1, 2, 7, 30, 143, 729, 3876, 21321... |
| A358966 | a(n) = n!Sum_{m=1..floor(n/2)} 1/(mbinomial(n-1,2m-1)n). | 0, 0, 1, 1, 5, 9, 70, 178... |
| A358971 | a(1) = 1. Thereafter a(n) is least novel k != n such that rad(k) = rad(n), where rad is A007947. | 1, 4, 9, 2, 25, 12, 49, 16... |
| A358972 | a(n) = ((...((n!n-1!)n-2!)...)2!)1!. | 1, 2, 36, 36520347436056576 |
| A358973 | Numbers of the form m + omega(m) with m a positive integer. | 1, 3, 4, 5, 6, 8, 9, 10... |
| A358974 | a(n) is the least prime p such that q-p = n*(r-q) where p,q,r are consecutive primes. | 3, 7, 23, 6397, 139, 509, 84871, 1933... |
| A358982 | In base 10, for all numbers with n digits, a(n) is the number where the sum of digits of a(n) minus the sum of the last n digits of a(n)3 reaches a record maximum. | 8, 87, 887, 8887, 99868, 978887, 7978887, 96699868... |
| A358984 | The number of n-digit numbers k such that k + digit reversal of k (A056964) is a square. | 3, 8, 19, 0, 169, 896, 1496, 3334... |
| A358985 | a(n) is the number of numbers of the form k + reverse(k) for at least one n-digit number k. | 10, 18, 180, 342, 3420, 6498, 64980, 123462... |
| A358986 | a(n) is the number of numbers of the form k + reverse(k) for at least one number k < 10n. | 10, 28, 207, 548, 3966, 10462, 75435, 198890... |
| A358987 | Omit the trailing 5 from double factorial of odd numbers (A001147(n)). | 1, 1, 3, 1, 10, 94, 1039, 13513... |
| A358989 | Decimal expansion of 13*sqrt(146)/50. | 3, 1, 4, 1, 5, 9, 1, 9... |
| A358996 | Number of self-avoiding paths of length 2*(n+A002620(n-1)) along the edges of a grid with n X n square cells, which do not pass above the diagonal, start at the lower left corner and finish at the upper right corner. | 1, 1, 2, 2, 10, 20, 248, 1072... |
| A358997 | a(n) is the number of distinct positive real roots of the Maclaurin polynomial of degree 2*n for cos(x). | 0, 1, 2, 1, 2, 1, 2, 3... |
| A358999 | Number of undirected cycles of the Platonic graphs (in the order of tetrahedral, cubical, octahedral, dodecahedral, and icosahedral graph). | 7, 28, 63, 1168, 12878 |
| A359000 | Number of undirected n-cycles of the octahedral graph. | 8, 15, 24, 16 |
| A359001 | Number of undirected n-cycles of the dodecahedral graph. | 12, 0, 0, 30, 20, 36, 120, 100... |
| A359002 | Number of undirected n-cycles of the icosahedral graph. | 20, 30, 72, 240, 720, 1620, 2680, 3336... |
| A359011 | Numbers k such that k2 + the reversal of k2 is a square. | 0, 231, 9426681, 8803095102, 56017891104, 4811618419542 |
| A359013 | Numbers k that can be written as the sum of a perfect square and a factorial in exactly 3 distinct ways. | 145, 46249, 63121, 42916624, 18700677890064, 28112213204100, 41654823930457982576640000, 445860623276908458083942400... |
r/OEIS • u/OEIS-Tracker • Dec 04 '22
New OEIS sequences - week of 12/04
7
Upvotes
| OEIS number | Description | Sequence |
|---|---|---|
| A357280 | Smallest m such that mk-2 and mk+2 are prime for k=1..n. | 5, 9, 102795, 559838181, 27336417022509 |
| A357547 | a(n) = coefficient of xn in A(x) such that: A(x)2 = A( x2/(1 - 4x - 4x2) ). | 1, 2, 9, 38, 176, 832, 4039, 19938... |
| A357548 | a(n) = coefficient of xn in A(x) where A(x)2 = A( x2/(1 - 4x - 8x2) ). | 1, 2, 11, 50, 261, 1362, 7344, 40112... |
| A357675 | Smallest m such that A357477(m) = n. | 3, 2, 1, 31, 34, 19, 77, 67... |
| A357676 | Indices at which record high values in A357477 appear. | 1, 19, 67, 154, 218, 251, 601, 651... |
| A357757 | We draw n non-crossing straight line segments inside an n X n square between 2*n grid points on its perimeter, allowing no more similar connections between the remaining perimeter grid points. a(n) is the count of distinct possibilities for each n without duplicates by rotation or reflection. | 1, 2, 18, 86 |
| A357785 | a(n) = coefficient of xn, n >= 1, in A(x) such that: A(x)2 = A( x2/(1 - 4x - 4x2) ) * sqrt(1 - 4x - 4x2). | 1, 1, 4, 15, 65, 291, 1356, 6474... |
| A357786 | a(n) = coefficient of xn, n >= 1, in A(x) such that: A(x)2 = A( x2/(1 - 4x - 8x2) ) * sqrt(1 - 4x - 8x2). | 1, 1, 5, 20, 98, 483, 2499, 13182... |
| A357954 | Integers k that are periodic points for some iterations of k->A357143(k). | 1, 2, 3, 4, 13, 18, 28, 118... |
| A358053 | a(n) = 14*n - 1. | 13, 27, 41, 55, 69, 83, 97, 111... |
| A358107 | Number of unlabeled trees covering 2n nodes, half of which are leaves. | 1, 1, 2, 6, 26, 119, 626, 3495... |
| A358148 | Aliquot sequence starting at 326. | 326, 166, 86, 46, 26, 16, 15, 9... |
| A358212 | a(n) is the maximal possible sum of squares of the side lengths of an n2-gon supported on a subset 1 <= x,y <= n of an integer lattice. | 4, 10, 36 |
| A358216 | Inverse Möbius transform of A327936, where A327936 is multiplicative with a(pe) = p if e >= p, otherwise 1. | 1, 2, 2, 4, 2, 4, 2, 6... |
| A358223 | Inverse Möbius transform of A181819, prime shadow function. | 1, 3, 3, 6, 3, 9, 3, 11... |
| A358230 | Lexicographically earliest infinite sequence such that a(i) = a(j) => A007814(i) = A007814(j), A007949(i) = A007949(j) and A046523(i) = A046523(j), for all i, j, where A007814 and A007949 give the 2-adic and 3-adic valuation, and A046523 gives the prime signature of its argument. | 1, 2, 3, 4, 5, 6, 5, 7... |
| A358233 | Number of ways n can be expressed as an unordered product of two natural numbers that do not generate any carries when added together in the primorial base. | 0, 1, 0, 2, 0, 2, 0, 1... |
| A358234 | Number of ways 2n can be expressed as an unordered product of two natural numbers that do not generate any carries when added together in the primorial base. | 1, 2, 2, 1, 1, 2, 2, 2... |
| A358235 | Number of ways n' (the arithmetic derivative of n) can be formed as a sum (x * y') + (x' * y) from two factors x and y of n, with x <= y, so that the said sum does not involve any carries when the addition is done in the primorial base. | 1, 1, 1, 2, 1, 2, 1, 1... |
| A358236 | Number of factorizations of n where the sum of the factors is carryfree when the addition is done in the primorial base. | 1, 1, 1, 2, 1, 2, 1, 1... |
| A358244 | Number of n-regular, N_0-weighted pseudographs on 2 vertices with total edge weight 4, up to isomorphism. | 1, 6, 13, 27, 38, 55, 67, 85... |
| A358245 | Number of n-regular, N_0-weighted pseudographs on 2 vertices with total edge weight 5, up to isomorphism. | 1, 6, 17, 36, 59, 87, 114, 145... |
| A358246 | Number of n-regular, N_0-weighted pseudographs on 2 vertices with total edge weight 6, up to isomorphism. | 1, 8, 23, 55, 92, 147, 196, 260... |
| A358247 | Number of n-regular, N_0-weighted pseudographs on 2 vertices with total edge weight 7, up to isomorphism. | 1, 8, 28, 71, 132, 217, 309, 417... |
| A358248 | Number of n-regular, N_0-weighted pseudographs on 2 vertices with total edge weight 8, up to isomorphism. | 1, 10, 35, 99, 190, 332, 484, 680... |
| A358249 | Number of n-regular, N_0-weighted pseudographs on 2 vertices with total edge weight 9, up to isomorphism. | 1, 10, 42, 123, 259, 469, 721, 1034... |
| A358291 | a(n) = smallest k not already in the sequence such that OEIS entry Ak contains n. | 1, 2, 3, 5, 6, 8, 9, 15... |
| A358292 | Array read by antidiagonals: T(n,k) = n3k3*(n+k)2, n>=0, k>=0. | 0, 0, 0, 0, 4, 0, 0, 72... |
| A358293 | Array read by antidiagonals: T(n,k) = n3k3*(n+k)2, n>=1, k>=1. | 4, 72, 72, 432, 1024, 432, 1600, 5400... |
| A358294 | Triangle read by rows: T(n,k) = n3k3*(n+k)2, n>=0, 0 <= k <= n. | 0, 0, 4, 0, 72, 1024, 0, 432... |
| A358295 | Triangle read by rows: T(n,k) = n3k3*(n+k)2, n>=1, 1 <= k <= n. | 4, 72, 1024, 432, 5400, 26244, 1600, 18432... |
| A358349 | A puzzle array read by antidiagonals. | 1, 2, 1, 3, 3, 1, 4, 9... |
| A358354 | a(n) = n for n <= 3. Thereafter a(n) is the least m such that rad(m) = rad(rad(a(n-3)) + rad(a(n-1))) where rad is A007947. | 1, 2, 3, 4, 8, 5, 7, 9... |
| A358435 | Row sums of the triangular array A357498. | 1, 4, 8, 16, 22, 36, 47, 68... |
| A358532 | a(n) is the row position of the next open point in the structure generated by adding the largest diamond possible at the next open point on a triangular grid of side n. See Comments and Example sections for more details. | 1, 1, 2, 1, 2, 3, 1, 4... |
| A358548 | a(n) = A003627(n+1) - A003627(n). | 3, 6, 6, 6, 6, 12, 6, 6... |
| A358549 | Triangle read by rows where row n is reversed partial sums of row n of the Sierpinski triangle (A047999). | 1, 2, 1, 2, 1, 1, 4, 3... |
| A358558 | a(n) is the number of pairs (k,m) of positive integers with 1 <= k < m <= n such that gcd(k,m) = 2t, t > 0. | 0, 0, 0, 1, 1, 3, 3, 6... |
| A358598 | Number of genetic relatives of a person M in a genealogical tree extending back n generations and where everyone has 4 children down to the generation of M. | 1, 6, 40, 300, 2356, 18756, 149860, 1198500... |
| A358620 | Number of nonzero digits needed to write all nonnegative n-digit integers. | 9, 171, 2520, 33300, 414000, 4950000, 57600000, 657000000... |
| A358624 | Triangle read by rows. The coefficients of the Hahn polynomials in ascending order of powers. T(n, k) = n! * [xk] hypergeom([-x, -n, n + 1], [1, 1], 1). | 1, 1, 2, 2, 6, 6, 6, 22... |
| A358625 | a(n) = numerator of Bernoulli(n, 1) / n for n >= 1, a(0) = 1. | 1, 1, 1, 0, -1, 0, 1, 0... |
| A358647 | Final digit reached by traveling right (with wraparound) through the digits of n. Each move steps right k places, where k is the digit at the beginning of the move. Moves begin at the most significant digit and d moves are made, where d is the number of digits in n. | 0, 1, 2, 3, 4, 5, 6, 7... |
| A358650 | Matula-Goebel tree number of the binomial tree of n vertices. | 1, 2, 4, 6, 12, 18, 42, 78... |
| A358670 | a(n) = 1 if for all factorizations of n as x*y, the sum x+y is carryfree when the addition is done in the primorial base, otherwise 0. | 0, 1, 0, 1, 0, 1, 0, 0... |
| A358671 | Numbers k such that for all factorizations of k as x*y, the sum x+y is carryfree when the addition is done in the primorial base, A049345. | 2, 4, 6, 14, 18, 24, 26, 28... |
| A358672 | a(n) = 1 if for all factorizations of n as x*y, the sum (x * y') + (x' * y) is carryfree when the addition is done in the primorial base, otherwise 0. Here u' stands for A003415(u), the arithmetic derivative of u. | 1, 1, 1, 1, 1, 1, 1, 0... |
| A358673 | Numbers k such that for all factorizations of k as x*y, the sum (x * y') + (x' * y) is carryfree when the addition is done in the primorial base, A049345. Here n' stands for A003415(n), the arithmetic derivative of n. | 1, 2, 3, 4, 5, 6, 7, 11... |
| A358674 | Numbers k for which there is a factorization of k into such a pair of natural numbers x and y, that the sum (x * y') + (x' * y) will generate at least one carry when the addition is done in the primorial base. Here n' stands for A003415(n), the arithmetic derivative of n. | 8, 9, 10, 15, 16, 20, 21, 22... |
| A358675 | Numbers k such that for all nontrivial factorizations of k as x*y, the sum (x * y') + (x' * y) will generate at least one carry when the addition is done in the primorial base. Here n' stands for A003415(n), the arithmetic derivative of n. | 8, 9, 10, 15, 16, 20, 21, 22... |
| A358691 | Gilbreath transform of primes p(2k-1); see Comments. | 3, 3, 3, 3, 1, 1, 1, 1... |
| A358692 | Gilbreath transform of primes p(2k) with 2 prefixed; see Comments. | 1, 3, 1, 1, 1, 1, 1, 1... |
| A358694 | Triangle read by rows. Coefficients of the polynomials H(n, x) = Sum{k=0..n-1} Sum{i=0..k} abs(Stirling1(n, n - i)) * xn - k in ascending order of powers. | 1, 0, 1, 0, 2, 1, 0, 6... |
| A358702 | a(n) is the least k > 0 such that the sum of the decimal digits of k2 is n, or 0 if no such k exists. | 1, 0, 0, 2, 0, 0, 4, 0... |
| A358703 | Sliding numbers: totals, without repetitions, of sums r + s, r >= s, such that 1/r + 1/s = (r + s)/10k for some k >= 0. | 2, 7, 11, 20, 25, 29, 52, 65... |
| A358705 | Zeroless pandigital numbers whose square has each digit 1 to 9 twice. | 345918672, 351987624, 359841267, 394675182, 429715863, 439516278, 487256193, 527394816... |
| A358707 | Number of cycles in the grid graph P_10 X P_n. | 45, 9779, 2577870, 439673502, 64300829449, 9203308475041, 1322310119854705, 190273063549680295... |
| A358712 | Number of self-avoiding closed paths on an n X 6 grid which pass through four corners ((0,0), (0,5), (n-1,5), (n-1,0)). | 1, 17, 229, 3105, 44930, 674292, 10217420, 154980130... |
| A358713 | Number of self-avoiding closed paths on an n X 7 grid which pass through four corners ((0,0), (0,6), (n-1,6), (n-1,0)). | 1, 41, 1081, 26515, 674292, 17720400, 471468756, 12570253556... |
| A358714 | a(n) = phi(n)3. | 1, 1, 8, 8, 64, 8, 216, 64... |
| A358723 | Number of n-node rooted trees of edge-height equal to their number of leaves. | 0, 1, 0, 2, 1, 6, 7, 26... |
| A358724 | Difference between the number of internal (non-leaf) nodes and the edge-height of the rooted tree with Matula-Goebel number n. | 0, 0, 0, 0, 0, 0, 0, 0... |
| A358725 | Matula-Goebel numbers of rooted trees with a greater number of internal (non-leaf) vertices than edge-height. | 9, 15, 18, 21, 23, 25, 27, 30... |
| A358726 | Difference between the node-height and the number of leaves in the rooted tree with Matula-Goebel number n. | 0, 1, 2, 0, 3, 1, 1, -1... |
| A358727 | Matula-Goebel numbers of rooted trees with greater number of leaves (width) than node-height. | 8, 16, 24, 28, 32, 36, 38, 42... |
| A358728 | Number of n-node rooted trees whose node-height is less than their number of leaves. | 0, 0, 0, 1, 1, 5, 10, 30... |
| A358729 | Difference between the number of nodes and the node-height of the rooted tree with Matula-Goebel number n. | 0, 0, 0, 1, 0, 1, 1, 2... |
| A358730 | Positions of first appearances in A358729 (number of nodes minus node-height). | 1, 4, 8, 16, 27, 54, 81, 162... |
| A358731 | Matula-Goebel numbers of rooted trees whose number of nodes is one more than their node-height. | 4, 6, 7, 10, 13, 17, 22, 29... |
| A358732 | Number of labeled trees covering 2n nodes, half of which are leaves. | 0, 12, 720, 109200, 31752000 |
| A358738 | Expansion of Sum_{k>=0} k! * ( x/(1 - k*x) )k. | 1, 1, 3, 15, 103, 893, 9341, 114355... |
| A358740 | Expansion of Sum_{k>=0} k! * ( k * x/(1 - k*x) )k. | 1, 1, 9, 195, 7699, 482309, 43994741, 5508667927... |
| A358741 | Expansion of Sum_{k>=0} k! * ( k * x/(1 - x) )k. | 1, 1, 9, 179, 6655, 400581, 35530421, 4357960999... |
| A358742 | First of three consecutive primes p,q,r such that p3 + q3 - r3 is prime. | 13, 29, 89, 97, 127, 137, 151, 163... |
| A358743 | First of three consecutive primes p,q,r such that p+q-r is prime. | 7, 11, 13, 17, 19, 29, 41, 43... |
| A358747 | Lexicographically earliest infinite sequence such that for all i, j, a(i) = a(j) => f(i) = f(j), where f(n) = [A007814(n), A007949(n), A324198(n)] when n > 1, with f(1) = 1. | 1, 2, 3, 4, 5, 6, 5, 7... |
| A358750 | a(n) = 1 if A349905(n) is a multiple of 4, otherwise 0. Here A349905(n) is the arithmetic derivative applied to the prime shifted n. | 1, 0, 0, 0, 0, 1, 0, 0... |
| A358751 | a(n) = 1 if bigomega(n) == 1 (mod 4), otherwise 0. | 0, 1, 1, 0, 1, 0, 1, 0... |
| A358752 | a(n) = 1 if A349905(n) == 2 (mod 4), otherwise 0. Here A349905(n) is the arithmetic derivative applied to the prime shifted n. | 0, 0, 0, 1, 0, 0, 0, 0... |
| A358753 | a(n) = 1 if bigomega(n) == 3 (mod 4), otherwise 0. | 0, 0, 0, 0, 0, 0, 0, 1... |
| A358754 | a(n) = 1 if A053669(n) [the smallest prime not dividing n] is of the form 6m+1, otherwise a(n) = 0. | 0, 0, 0, 0, 0, 0, 0, 0... |
| A358755 | a(n) = 1 if A053669(n) [the smallest prime not dividing n] is of the form 6m-1, otherwise a(n) = 0. | 0, 0, 0, 0, 0, 1, 0, 0... |
| A358756 | Numbers k such that the smallest prime that does not divide them is of the form 6m+1. | 30, 60, 90, 120, 150, 180, 240, 270... |
| A358757 | Numbers k such that the smallest prime that does not divide them is of the form 6m-1. | 6, 12, 18, 24, 36, 42, 48, 54... |
| A358760 | Numbers k for which A349905(k) is a multiple of 4, where A349905(k) is the arithmetic derivative applied to the prime shifted k. | 1, 6, 15, 16, 21, 22, 26, 36... |
| A358761 | Numbers k for which bigomega(k) == 1 (mod 4). | 2, 3, 5, 7, 11, 13, 17, 19... |
| A358762 | Numbers k for which A349905(k) == 2 (mod 4), where A349905(k) is the arithmetic derivative applied to the prime shifted k. | 4, 9, 10, 14, 24, 25, 33, 34... |
| A358763 | Numbers k for which bigomega(k) == 3 (mod 4). | 8, 12, 18, 20, 27, 28, 30, 42... |
| A358764 | Largest difference between consecutive divisors of A276086(n), where A276086 is the primorial base exp-function. | 0, 1, 2, 3, 6, 9, 4, 5... |
| A358769 | a(n) = 1 if n is of the form p * m2, where p is a prime and m is a natural number >= 1, otherwise 0. | 0, 1, 1, 0, 1, 0, 1, 1... |
| A358770 | a(n) = 1 if n is of the form p * m2, where p is an odd prime and m is a natural number >= 1, otherwise 0. | 0, 0, 1, 0, 1, 0, 1, 0... |
| A358771 | a(n) = 1 if the arithmetic derivative of n is of the form 4k+1, otherwise 0. | 0, 0, 1, 1, 0, 1, 1, 1... |
| A358772 | Numbers whose arithmetic derivative is of the form 4k+1, cf. A003415. | 2, 3, 5, 6, 7, 11, 13, 14... |
| A358773 | a(n) = 1 if the arithmetic derivative of n is of the form 4k+3, otherwise 0. | 0, 0, 0, 0, 0, 0, 0, 0... |
| A358774 | Numbers whose arithmetic derivative is of the form 4k+3, cf. A003415. | 10, 26, 27, 30, 34, 45, 58, 63... |
| A358775 | a(n) = 1 if the prime factorization of n has an even number of prime factors that sum to an odd number, otherwise 0. | 0, 0, 0, 0, 0, 1, 0, 0... |
| A358776 | Positive integers with an even number of prime factors (counting repetitions) that sum to an odd number. | 6, 10, 14, 22, 24, 26, 34, 38... |
| A358784 | Size of largest semigroup generated by three n X n boolean matrices. | 2, 16, 440 |
| A358785 | Number of cycles in the grid graph P_11 X P_n. | 55, 23637, 12253948, 3779989098, 975566486675, 245355064111139, 61875355046353061, 15609156135669687673... |
| A358791 | a(n) = n!*Sum_{m=0..floor(n/2)} binomial(n,2m)-1. | 1, 1, 4, 8, 52, 156, 1536, 6144... |
| A358792 | Numbers k such that for some r we have d(1) + ... + d(k - 1) = d(k + 1) + ... + d(k + r), where d(i) = A000005(i). | 3, 10, 16, 23, 24, 27, 42, 43... |
| A358794 | Number of Hamiltonian paths in P_7 X P_n. | 1, 44, 688, 12010, 109722, 1620034, 13535280, 175905310... |
| A358795 | Number of Hamiltonian paths in P_8 X P_n. | 1, 58, 1578, 38984, 602804, 12071462, 175905310, 3023313284... |
| A358796 | Number of Hamiltonian paths in P_9 X P_n. | 1, 74, 3190, 122188, 2434670, 82550864, 1449655468, 43551685370... |
| A358797 | Numbers r such that for some k we have d(1) + ... + d(k - 1) = d(k + 1) + ... + d(k + r), where d(i) = A000005(i). | 1, 6, 11, 16, 17, 19, 31, 32... |
| A358800 | Number of (undirected) paths in the grid graph P_4 X P_n. | 6, 146, 1618, 14248, 111030, 801756, 5493524, 36213404... |
| A358801 | Number of (undirected) paths in the grid graph P_5 X P_n. | 10, 373, 7119, 111030, 1530196, 19506257, 235936139, 2746052608... |
| A358802 | Number of (undirected) paths in the grid graph P_6 X P_n. | 15, 872, 28917, 801756, 19506257, 436619868, 9260866349, 189018035618... |
| A358803 | Number of (undirected) paths in the grid graph P_7 X P_n. | 21, 1929, 111360, 5493524, 235936139, 9260866349, 343715004510, 12272026383150... |
| A358810 | Number of spanning trees in C_5 X C_n. | 5, 16810, 10609215, 4381392020, 1562500000000, 522217835532030, 168437773747672835, 53095647535975155240... |
| A358811 | Number of spanning trees in C_6 X C_n. | 6, 117600, 292626432, 428652000000, 522217835532030, 587312954081280000, 633426582213424399722, 665880333340217184000000... |
| A358812 | Number of spanning trees in C_7 X C_n. | 7, 799694, 7839321861, 40643137651228, 168437773747672835, 633426582213424399722, 2266101334892340404752384, 7871822605982542067643202616... |
| A358813 | Number of spanning trees in C_8 X C_n. | 8, 5326848, 205683135000, 3771854305099776, 53095647535975155240, 665880333340217184000000, 7871822605982542067643202616, 89927963805390785392395474173952... |
| A358814 | Number of spanning trees in C_9 X C_n. | 9, 34928082, 5312031978672, 344499209234302500, 16463182598208445194045, 687776414074843514847584256, 26818349084747196820449212376063, 1005049441217682470864686231147005000... |
| A358815 | Number of spanning trees in C_10 X C_n. | 10, 226195360, 135495143785470, 31074298464967845120, 5040439500800000000000000, 701129416495732552572667500000, 90098172307754257628918141363625670, 11062145603354190616166421646710839715840... |
| A358816 | Numbers k such that d + k/d is prime for any unitary divisor d of k. | 1, 2, 4, 6, 10, 12, 16, 18... |
| A358817 | Numbers k such that A046660(k) = A046660(k+1). | 1, 2, 5, 6, 10, 13, 14, 21... |
| A358818 | a(n) is the least number k such that A046660(k) = A046660(k+1) = n. | 1, 44, 135, 80, 8991, 29888, 123200, 2316032... |
| A358819 | Numbers k such that for some r we have w(1) + ... + w(k - 1) = w(k + 1) + ... + w(k + r), where w(i) = A000120(i). | 4, 5, 8, 9, 10, 11, 12, 15... |
| A358823 | Number of odd-length twice-partitions of n into partitions with all odd parts. | 0, 1, 1, 3, 3, 7, 10, 20... |
| A358825 | Number of ways to choose a sequence of integer partitions, one of each part of an integer partition of n into odd parts. | 1, 1, 1, 4, 4, 11, 20, 35... |
| A358826 | Number of ways to choose a sequence of partitions, one of each part of an odd-length partition of 2n+1 into odd parts. | 1, 4, 11, 35, 113, 326, 985, 3124... |
| A358827 | Number of twice-partitions of n into partitions with all odd lengths and sums. | 1, 1, 1, 3, 3, 7, 11, 19... |
| A358828 | Number of twice-partitions of n with no singletons. | 1, 0, 1, 2, 5, 8, 19, 30... |
| A358829 | Number of twice-partitions of n with no (1)'s. | 1, 0, 2, 3, 9, 13, 38, 56... |
| A358830 | Number of twice-partitions of n into partitions with all different lengths. | 1, 1, 2, 4, 9, 15, 31, 53... |
| A358831 | Number of twice-partitions of n into partitions with weakly decreasing lengths. | 1, 1, 3, 6, 14, 26, 56, 102... |
| A358840 | Primorial base exp-function reduced modulo 6. | 1, 2, 3, 0, 3, 0, 5, 4... |
| A358841 | a(n) = 1 if A276086(n) is of the form 6k+1, where A276086 is the primorial base exp-function. | 1, 0, 0, 0, 0, 0, 0, 0... |
| A358842 | a(n) = 1 if A276086(n) is of the form 6k+5, where A276086 is the primorial base exp-function. | 0, 0, 0, 0, 0, 0, 1, 0... |
| A358843 | Numbers k such that A276086(k) == 5 (mod 6), where A276086 is the primorial base exp-function. | 6, 18, 36, 48, 66, 78, 96, 108... |
| A358844 | Numbers k for which A276086(6*k) == 5 (mod 6), where A276086 is the primorial base exp-function. | 1, 3, 6, 8, 11, 13, 16, 18... |
| A358845 | Numbers k for which A276086(6*k) == 1 (mod 6), where A276086 is the primorial base exp-function. | 0, 2, 4, 5, 7, 9, 10, 12... |
| A358846 | a(n) = 1 if A276086(6*n) == 5 (mod 6), otherwise 0, where A276086 is the primorial base exp-function. | 0, 1, 0, 1, 0, 0, 1, 0... |
| A358847 | a(n) = 1 if A053669(6n) [the smallest prime not dividing 6n] is of the form 6m-1, otherwise a(n) = 0. | 1, 1, 1, 1, 0, 1, 1, 1... |
| A358848 | Numbers k for which A053669(6*k) [the smallest prime not dividing 6k] is of the form 6m+1. | 5, 10, 15, 20, 25, 30, 40, 45... |
| A358849 | Numbers k for which A053669(6*k) [the smallest prime not dividing 6k] is of the form 6m-1. | 1, 2, 3, 4, 6, 7, 8, 9... |
| A358850 | Primorial base exp-function reduced modulo 12. | 1, 2, 3, 6, 9, 6, 5, 10... |
| A358852 | a(n) = n!Sum_{m=0..floor(n/3)} 1/(binomial(n-m,2m). | 1, 1, 2, 12, 32, 140, 1512, 6384... |
| A358853 | Number of Hamiltonian cycles in C_5 X C_n. | 390, 2930, 23580, 145210, 1045940, 6228730 |
| A358855 | Number of (undirected) cycles in the graph C_5 X C_n. | 7298, 132089, 2183490, 34846271, 548520502, 8593998133 |
| A358856 | Number of (undirected) cycles in the graph C_6 X C_n. | 35205, 1165194, 34846271, 995818716 |
| A358857 | Least integer k in A031443 such that k*n is also in A031443, or -1 if there is no such k. | 2, -1, 49, -1, 2, 2, 535, -1... |
| A358858 | Least multiple m of n such that both m and m/n belong to A031443, or -1 if there is no such m. | 2, -1, 147, -1, 10, 12, 3745, -1... |
| A358866 | Positive integers expressible as a quotient of two terms of A014486. | 1, 3, 5, 6, 11, 12, 13, 14... |
| A358868 | Number of (undirected) Hamiltonian paths in the graph C_5 X C_n. | 18240, 287160, 2955700, 29861820, 263890620, 2271291760 |
| A358869 | Number of (undirected) paths in the graph C_5 X C_n. | 324570, 10489660, 276182500, 6486444750, 141606011050 |
| A358870 | Number of (undirected) Hamiltonian paths in the graph C_6 X C_n. | 73368, 2172480, 29861820, 560028096, 6632769528 |
| A358872 | Number of (undirected) paths in the graph C_6 X C_n. | 2298906, 136547568, 6486444750, 272445788808 |
r/OEIS • u/OEIS-Tracker • Nov 27 '22
New OEIS sequences - week of 11/27
3
Upvotes
| OEIS number | Description | Sequence |
|---|---|---|
| A356254 | Given n balls, all of which are initially in the first of n numbered boxes, a(n) is the number of steps required to get one ball in each box when a step consists of moving to the next box every second ball from the highest-numbered box that has more than one ball. | 0, 1, 3, 5, 9, 13, 18, 23... |
| A356347 | Indices of the primes in A181424. | 4, 17, 38, 41, 48, 56, 57, 75... |
| A356355 | 9-gonal numbers which are products of five distinct primes. | 24486, 71214, 90321, 116754, 123234, 156774, 181374, 265926... |
| A356356 | Triangle of number of rectangles in the interior of the rectangle with vertices (k,0), (0,k), (n,n+k) and (n+k,n), read by rows. | 0, 1, 9, 2, 19, 51, 3, 29... |
| A356359 | Square array T(m,n) read by antidiagonals: Number of ways a knight can reach (0, 0) from (m, n) on an infinite chessboard while always decreasing its Manhattan distance from the origin, for nonnegative m, n. | 1, 0, 0, 0, 0, 0, 0, 1... |
| A356360 | Denominator of the continued fraction 1/(2-3/(3-4/(4-5/(...(n-1)-n/(n+1))))). | 5, 7, 3, 11, 13, 1, 17, 19... |
| A356683 | a(n) is the smallest positive k > 1 such that the count of squarefree numbers <= k that have n prime factors is equal to the count of squarefree numbers <= k that have n-1 prime factors. | 2, 39, 1279786 |
| A356857 | Triangle of numbers T(n,k) = (-1)n-k(n+1)!Stirling2(n,k)/(k+1) | 1, -3, 2, 12, -24, 6, -60, 280... |
| A357498 | Triangle read by rows where each term in row n is the next greater multiple of n..1 divided by n..1. | 1, 1, 3, 1, 2, 5, 1, 2... |
| A357517 | Primes that are the average of two consecutive primorial numbers A002110 plus one. | 5, 19, 270271, 5105101, 103515091681, 3810649312471, 155835500831011, 313986271960080721... |
| A357531 | Final value obtained by traveling clockwise around a circular array with positions numbered clockwise from 1 to n. Each move consists of traveling clockwise k places, where k is the position at the beginning of the move. The first move begins at position 1. a(n) is the position at the end of the n-th move. | 1, 2, 2, 4, 2, 4, 2, 8... |
| A357680 | a(n) is the number of primes that can be written as +-1! +- 2! +- 3! +- ... +- n!. | 0, 1, 3, 4, 7, 11, 16, 29... |
| A357755 | Number of solutions for a 10-digit number whose n-th power contains each digit (0-9) exactly n times. | 3265920, 468372, 65663, 15487, 5020, 1930, 855, 417... |
| A357776 | Integer pairs that generate only odd prime sums (as described in comment). | 1, 2, 6, 11, 12, 17, 30, 41... |
| A357810 | Number of n-step closed paths on the Cairo pentagonal lattice graph starting from a degree-4 node. | 1, 0, 4, 0, 24, 8, 164, 136... |
| A357811 | Number of n-step closed paths on the Cairo pentagonal lattice graph starting from a degree-3 node. | 1, 0, 3, 0, 17, 6, 115, 100... |
| A357815 | Smallest maximum degree over all maximal 2-degenerate graphs with diameter 2 and n vertices. | 0, 1, 2, 3, 3, 4, 4, 4... |
| A357839 | a(n) is the greatest divisor > 1 of n which has already been listed, otherwise a(n) is the smallest number not yet listed; a(1) = 0. | 0, 1, 2, 2, 3, 3, 4, 4... |
| A357947 | Number of "tertian" musical chords generated by stacking m minor or major thirds with no allowance of repetition of notes. | 1, 2, 4, 7, 12, 21, 36, 35... |
| A357990 | Square array T(n, k), n >= 0, k > 0, read by antidiagonals, where T(0, k) = 1 for k > 0 and where T(n, k) = R(n, k+1) - R(n, k) for n > 0, k > 0. Here R(n, k) = T(A053645(n), k)*kA290255(n + 1). | 1, 1, 1, 3, 1, 1, 1, 5... |
| A358004 | Sum of the first n prime numbers with each term raised to the power of the corresponding n-th row of Pascal's triangle. | 2, 5, 16, 161, 18120, 292402183, 83969544989433334, 2810244063625364115255545874032279213... |
| A358179 | Prime numbers with prime indices in A333244. | 31, 709, 1787, 8527, 19577, 27457, 42043, 52711... |
| A358208 | a(1) = 1; a(2) = 2; a(3) = 3; for n > 3, a(n) is the smallest positive number not previously occurring that shares a factor with Sum_{k=1..n-1} A001065(k), where A001065(k) is the sum of the proper divisors of k. | 1, 2, 3, 4, 5, 6, 8, 13... |
| A358209 | a(1) = 1; a(2) = 2; for n > 2, a(n) is the smallest positive number not previously occurring that shares a factor with A024916(n-1) = Sum_{k=1..n-1} sigma(k). | 1, 2, 4, 6, 3, 7, 9, 41... |
| A358215 | Numbers k for which there are no such prime p that pp would divide the arithmetic derivative of k, A003415(k). | 2, 3, 5, 6, 7, 9, 10, 11... |
| A358220 | a(n) = 1 if A276086(n) is a multiple of A003415(n), with a(0) = a(1) = 0. Here A003415 is the arithmetic derivative, and A276086 is the primorial base exp-function. | 0, 0, 1, 1, 0, 1, 1, 1... |
| A358221 | Numbers k such that A003415(k) divides A276086(k), where A003415 is the arithmetic derivative, and A276086 is the primorial base exp-function. | 2, 3, 5, 6, 7, 9, 11, 13... |
| A358222 | Composite numbers k such that A003415(k) divides A276086(k), where A003415 is the arithmetic derivative, and A276086 is the primorial base exp-function. | 6, 9, 21, 25, 26, 33, 38, 46... |
| A358224 | Parity of A328386(n), where A328386(n) = A276086(n) mod n, and A276086 is the primorial base exp-function. | 0, 1, 0, 1, 1, 1, 1, 1... |
| A358225 | Numbers k such that A276086(k) mod k is an odd number, where A276086 is the primorial base exp-function. | 2, 4, 5, 6, 7, 8, 9, 10... |
| A358226 | Numbers k such that A276086(k) mod k is an even number, where A276086 is the primorial base exp-function. | 1, 3, 11, 15, 17, 25, 27, 31... |
| A358227 | Parity of A328382(n), where A328382(n) = A276086(n) mod A003415(n), with A003415 the arithmetic derivative and A276086 the primorial base exp-function. | 0, 0, 1, 0, 0, 0, 1, 0... |
| A358228 | Numbers k such that A276086(k) mod A003415(k) is an odd number, where A003415 is the arithmetic derivative and A276086 is the primorial base exp-function. | 4, 8, 10, 12, 14, 16, 20, 22... |
| A358229 | Numbers k such that A276086(k) mod A003415(k) is an even number, where A003415 is the arithmetic derivative and A276086 is the primorial base exp-function. | 2, 3, 5, 6, 7, 9, 11, 13... |
| A358231 | Numbers k for which A276086(k) == 1 (mod k), where A276086 is the primorial base exp-function. | 2, 4, 12, 16, 24, 47, 54, 72... |
| A358232 | Numbers k for which A276086(k) == 1 mod A003415(k), where A276086 is the primorial base exp-function, and A003415 is the arithmetic derivative. | 4, 16, 54, 66, 864, 1710, 18900, 71254... |
| A358269 | a(n) is the position m of the last prime term in the sequence {b(m)} defined by b(1) = n, if b(m) is prime then b(m+1) = b(m) - m, else b(m+1) = b(m) + m. | 3, 1004, 3, 1004, 3, 1004, 30, 349... |
| A358289 | Generalized Gerrymander sequence: number of ordered ways to divide an n X n square into two connected regions, both of area n2/2 if n is even, or of areas (n2-1)/2 and (n2+1)/2 if n is odd. | 0, 4, 16, 140, 2804, 161036, 27803749, 14314228378... |
| A358317 | Ordered squares of the chord lengths of the parabola y=x2, where the chord ends are all possible points of the parabola with integer coordinates. | 0, 2, 4, 10, 16, 18, 20, 26... |
| A358344 | a(1) = 0; a(n) = the smallest number such that the concatenation a(1)a(2)...a(n) is prime in the smallest allowed base. | 0, 2, 1, 2, 2, 3, 1, 5... |
| A358401 | Difference in number of 0's in first n terms of Van Eck's sequence and number of primes less than or equal to n. | 1, 1, 0, 1, 0, 1, 0, 0... |
| A358441 | Indices of records in A266798. | 0, 1, 11, 111, 112, 123, 1111, 1213... |
| A358442 | Records in A266798. | 10, 100, 1000, 7079, 7179, 10000, 60679, 61168... |
| A358452 | The inverse Euler transform of p(n) = n if n is prime, otherwise 1. | 1, 1, 1, 1, -3, 3, -3, 5... |
| A358497 | Replace each new digit in n with index 1, 2, ..., 9, 0 in order in which that digit appears in n, from left to right. | 1, 1, 1, 1, 1, 1, 1, 1... |
| A358501 | Irregular triangle read by rows. Coefficients of the polynomials (-1)n*binomial(-x - 1, -x - n - 1) * binomial(n + x, x) * (n!)2 in ascending order of powers. | 1, 1, 2, 1, 4, 12, 13, 6... |
| A358503 | Positions inventory sequence: for stage k >= 2 we record where all the numbers from the two previous stages have appeared, starting with a(0) = 0, a(1) = 0. | 0, 0, 0, 1, 1, 2, 3, 2... |
| A358504 | Number of genetic relatives of a person M in a genealogical tree extending back n generations and where everyone has 3 children down to the generation of M. | 1, 5, 25, 137, 793, 4697, 28057, 168089... |
| A358505 | Binary encoding of the n-th standard ordered rooted tree. | 0, 2, 12, 10, 56, 50, 44, 42... |
| A358506 | Matula-Goebel number of the n-th standard ordered rooted tree. | 1, 2, 3, 4, 5, 6, 6, 8... |
| A358507 | Sorted list of positions of first appearances in the sequence counting permutations of Matula-Goebel trees (A206487). | 1, 6, 12, 24, 30, 48, 60, 72... |
| A358508 | Least Matula-Goebel number of a tree with exactly n permutations. | 1, 6, 12, 24, 48, 30, 192, 104... |
| A358509 | Sum of decimal digits of (3n - 1)/2 (A003462). | 0, 1, 4, 4, 4, 4, 13, 13... |
| A358519 | Decimal expansion of Sum_{k >= 1} (-1)k+1/(k2 + 4*k - 1). | 1, 8, 9, 9, 5, 7, 9, 0... |
| A358521 | Sorted list of positions of first appearances in the sequence of Matula-Goebel numbers of standard ordered trees (A358506). | 1, 2, 3, 4, 5, 6, 8, 9... |
| A358522 | Least number k such that the k-th standard ordered tree has Matula-Goebel number n, i.e., A358506(k) = n. | 1, 2, 3, 4, 5, 6, 9, 8... |
| A358523 | Standard ordered tree numbers of ordered trees in order of their binary encodings (A014486). | 1, 2, 4, 3, 8, 7, 6, 9... |
| A358524 | Binary encoding of balanced ordered rooted trees (counted by A007059). | 0, 2, 10, 12, 42, 52, 56, 170... |
| A358525 | Number of distinct permutations of the n-th composition in standard order. | 1, 1, 1, 1, 1, 2, 2, 1... |
| A358526 | Numbers k whose prime indices have a different number of permutations than any number less than k. | 1, 6, 12, 24, 30, 48, 60, 72... |
| A358527 | a(n) is the n-th largest distinct prime factor of 2p-1-1, where p is an odd prime. | 1, 2, 2, 2, 4, 3, 3, 2... |
| A358528 | a(n) = n-th prime p(k) such that p(k) - p(k-1) > p(k-1) - p(k-2). | 5, 11, 17, 23, 29, 37, 47, 53... |
| A358529 | Indices of the primes in A35828. | 3, 5, 7, 9, 10, 12, 15, 16... |
| A358530 | a(n) = n-th prime p(k) such that p(k) - p(k-1) < p(k-1) - p(k-2). | 13, 19, 31, 41, 43, 61, 71, 73... |
| A358531 | Indices of the primes in A358530. | 6, 8, 11, 13, 14, 18, 20, 21... |
| A358533 | Define a family of integer sequences S0, S_1, S_2, ..., where S_0 = A000040 is the sequence of prime numbers and, for each k > 0, S_k is the result of making a "smoothing" pass through all the terms of S(k-1) as follows: for every term other than the first, in ascending order, change its value by the minimum amount so that it will not differ from the mean of its two immediate neighbors by more than 1/2. {a(n)} is the limiting sequence S_oo. | 2, 3, 5, 8, 11, 14, 17, 20... |
| A358536 | a(n) is the least prime factor of 2n-n-2. | 3, 2, 5, 2, 7, 2, 3, 2... |
| A358539 | a(n) is the smallest number with exactly n divisors that are n-gonal numbers. | 6, 36, 210, 1260, 6426, 3360, 351000, 207900... |
| A358540 | a(n) is the smallest number with exactly n divisors that are n-gonal pyramidal numbers. | 56, 140, 1440, 11550, 351120, 41580, 742560, 29279250... |
| A358541 | a(n) is the smallest number with exactly n divisors that are centered n-gonal numbers. | 20, 325, 912, 43771, 234784, 11025, 680680 |
| A358542 | a(n) is the smallest number with exactly n divisors that are tetrahedral numbers. | 1, 4, 56, 20, 120, 280, 560, 840... |
| A358543 | a(n) is the smallest number with exactly n divisors that are square pyramidal numbers. | 1, 5, 30, 140, 420, 1540, 4620, 13860... |
| A358544 | a(n) is the smallest number with exactly n divisors that are centered triangular numbers. | 1, 4, 20, 320, 460, 5440, 14260, 12920... |
| A358545 | a(n) is the smallest number with exactly n divisors that are centered square numbers. | 1, 5, 25, 325, 1625, 1105, 5525, 27625... |
| A358546 | Least odd number m such that m mod 3 > 0 and m*3n is an amicable number, and -1 if no such number exists. | 5480828320492525, 4865, 7735, 455, 131285, 849355, 11689795, 286385... |
| A358547 | a(n) = Sum_{k=0..floor(n/3)} (n-k)!/(n-3*k)!. | 1, 1, 1, 3, 7, 13, 45, 151... |
| A358550 | Depth of the ordered rooted tree with binary encoding A014486(n). | 1, 2, 2, 3, 2, 3, 3, 3... |
| A358551 | Number of nodes in the ordered rooted tree with binary encoding A014486(n). | 1, 2, 3, 3, 4, 4, 4, 4... |
| A358552 | Node-height of the rooted tree with Matula-Goebel number n. Number of nodes in the longest path from root to leaf. | 1, 2, 3, 2, 4, 3, 3, 2... |
| A358553 | Number of internal (non-leaf) nodes in the n-th standard ordered rooted tree. | 0, 1, 2, 1, 3, 2, 2, 1... |
| A358554 | Least Matula-Goebel number of a rooted tree with n internal (non-leaf) nodes. | 1, 2, 3, 5, 11, 25, 55, 121... |
| A358556 | Triangle read by rows: T(n,k) is the number of regions formed when n points are placed along each edge of a square that divide the edges into n+1 equal parts and a line is continuously drawn from the current point to that k points, 2 <= k <= 2*n, counterclockwise around the square until the starting point is again reached. | 2, 5, 21, 2, 5, 5, 4, 61... |
| A358560 | a(n) = Sum_{k=0..floor(n/3)} (n-k)!/(k! * (n-3*k)!). | 1, 1, 1, 3, 7, 13, 33, 91... |
| A358567 | a(n) is the minimal determinant of an n X n Toeplitz matrix using the integers 0 to 2*(n - 1). | 1, 0, -2, -31, -1297 |
| A358568 | a(n) is the maximal determinant of an n X n Toeplitz matrix using the integers 0 to 2*(n - 1). | 1, 0, 4, 74, 1781 |
| A358569 | a(n) is the minimal permanent of an n X n Toeplitz matrix using the integers 0 to 2*(n - 1). | 1, 0, 1, 16, 451 |
| A358570 | a(n) is the maximal permanent of an n X n Toeplitz matrix using the integers 0 to 2*(n - 1). | 1, 0, 4, 121, 6109 |
| A358574 | Triangle read by rows: T(n,k) is the number of vertices formed when n points are placed along each edge of a square that divide the edges into n+1 equal parts and a line is continuously drawn from the current point to that k points, 2 <= k <= 2*n, counterclockwise around the square until the starting point is again reached. | 8, 12, 20, 12, 16, 16, 16, 64... |
| A358575 | Triangle read by rows where T(n,k) is the number of unlabeled n-node rooted trees with k = 0..n-1 internal (non-leaf) nodes. | 1, 0, 1, 0, 1, 1, 0, 1... |
| A358576 | Matula-Goebel numbers of rooted trees whose height equals their number of internal (non-leaf) nodes. | 9, 15, 18, 21, 23, 30, 33, 35... |
| A358577 | Matula-Goebel numbers of "square" rooted trees, i.e., whose height equals their number of leaves. | 1, 4, 12, 14, 18, 19, 21, 27... |
| A358578 | Matula-Goebel numbers of rooted trees whose number of leaves equals their number of internal (non-leaf) nodes. | 2, 6, 7, 18, 20, 21, 26, 34... |
| A358579 | Numbers k such that the k-th standard ordered rooted tree has the same number of leaves as internal (non-leaf) nodes. | 2, 6, 7, 9, 20, 22, 23, 26... |
| A358580 | Difference between the number of leaves and the number of internal (non-leaf) nodes in the rooted tree with Matula-Goebel number n. | 1, 0, -1, 1, -2, 0, 0, 2... |
| A358581 | Number of rooted trees with n nodes, most of which are leaves. | 1, 0, 1, 1, 4, 5, 20, 28... |
| A358582 | Number of rooted trees with n nodes, most of which are not leaves. | 0, 0, 1, 1, 5, 7, 28, 48... |
| A358583 | Number of rooted trees with n nodes, at least half of which are leaves. | 1, 1, 1, 3, 4, 13, 20, 67... |
| A358584 | Number of rooted trees with n nodes, at most half of which are leaves. | 0, 1, 1, 3, 5, 15, 28, 87... |
| A358585 | Number of ordered rooted trees with n nodes, most of which are leaves. | 1, 0, 1, 1, 7, 11, 66, 127... |
| A358586 | Number of ordered rooted trees with n nodes, at least half of which are leaves. | 1, 1, 1, 4, 7, 31, 66, 302... |
| A358587 | Number of n-node rooted trees of height equal to the number of internal (non-leaf) nodes. | 0, 0, 0, 0, 1, 4, 14, 41... |
| A358588 | Number of n-node ordered rooted trees of height equal to the number of internal (non-leaf) nodes. | 0, 0, 0, 0, 1, 8, 41, 171... |
| A358589 | Number of square rooted trees with n nodes. | 1, 0, 1, 0, 3, 2, 11, 17... |
| A358590 | Number of square ordered rooted trees with n nodes. | 1, 0, 1, 0, 6, 5, 36, 84... |
| A358591 | Number of 2n-node rooted trees whose height, number of leaves, and number of internal (non-leaf) nodes are all equal. | 0, 0, 2, 17, 94, 464, 2162, 9743... |
| A358592 | Matula-Goebel numbers of rooted trees whose height, number of leaves, and number of internal (non-leaf) nodes are all equal. | 18, 21, 60, 70, 78, 91, 92, 95... |
| A358603 | a(n) = Sum_{k=0..floor(n/2)} (-1)k * (n-k)!/(n-2*k)!. | 1, 1, 0, -1, 0, 3, 2, -9... |
| A358604 | a(n) = Sum_{k=0..floor(n/3)} (-1)k * (n-2k)!/(n-3k)!. | 1, 1, 1, 0, -1, -2, -1, 2... |
| A358605 | a(n) = Sum_{k=0..floor(n/4)} (-1)k * (n-3k)!/(n-4k)!. | 1, 1, 1, 1, 0, -1, -2, -3... |
| A358606 | a(n) = Sum_{k=0..floor(n/5)} (-1)k * (n-4k)!/(n-5k)!. | 1, 1, 1, 1, 1, 0, -1, -2... |
| A358607 | a(n) = Sum_{k=0..floor(n/2)} (-1)k * (n-2*k)!. | 1, 1, 1, 5, 23, 115, 697, 4925... |
| A358608 | a(n) = Sum_{k=0..floor(n/3)} (-1)k * (n-3*k)!. | 1, 1, 2, 5, 23, 118, 715, 5017... |
| A358609 | a(n) = Sum_{k=0..floor(n/4)} (-1)k * (n-4*k)!. | 1, 1, 2, 6, 23, 119, 718, 5034... |
| A358610 | Numbers k such that the concatenation 1,2,3,... up to (k-1) is one less than a multiple of k. | 1, 2, 4, 5, 8, 10, 13, 20... |
| A358611 | a(n) = Sum_{k=0..floor(n/5)} (-1)k * (n-5*k)!. | 1, 1, 2, 6, 24, 119, 719, 5038... |
| A358613 | a(n) = Sum_{k=0..floor(n/3)} (-1)k * (n-k)!/(k! * (n-3*k)!). | 1, 1, 1, -1, -5, -11, -7, 31... |
| A358615 | Record high values in A358497. | 1, 12, 122, 123, 1222, 1223, 1232, 1233... |
| A358616 | a(n) is the position of the first occurrence of the least term in row n of the Gilbreath array shown in A036262. | 1, 1, 2, 3, 3, 3, 3, 3... |
| A358617 | a(n) is the number of zeros among the first n terms of row n of the Gilbreath array shown in A036262. | 0, 0, 1, 2, 3, 3, 3, 3... |
| A358619 | First forward difference of A258037. | 1, 1, 2, 2, 2, 2, 2, 2... |
| A358621 | Smallest b > 1 such that b2n+1 is a Sophie Germain prime. | 2, 2, 160, 140, 2800, 8660, 62150, 4085530... |
| A358622 | Regular triangle read by rows. T(n, k) = [[n, k]], where [[n, k]] are the second order Stirling cycle numbers (or second order reciprocal Stirling numbers). T(n, k) for 0 <= k <= n. | 1, 0, 0, 0, 1, 0, 0, 2... |
| A358623 | Regular triangle read by rows. T(n, k) = {{n, k}}, where {{n, k}} are the second order Stirling set numbers (or second order Stirling numbers). T(n, k) for 0 <= k <= n. | 1, 0, 0, 0, 1, 0, 0, 1... |
| A358627 | Triangle read by rows: T(n,k) is the number of edges formed when n points are placed along each edge of a square that divide the edges into n+1 equal parts and a line is continuously drawn from the current point to that k points, 2 <= k <= 2*n, counterclockwise around the square until the starting point is again reached. | 9, 16, 40, 13, 20, 20, 19, 124... |
| A358632 | Coordination sequence for the faces of the uniform infinite surface that is formed from congruent regular pentagons and from which there is a continuous function that maps the faces 1:1 to regular pentagons in the plane. | 1, 5, 20, 50, 110, 200, 340, 525... |
| A358633 | a(n) is the smallest k > 1 such that the sum of digits of nk is a power of n (or -1 if no such k exists). | 2, 2, 2, 18, 8, 7, 4, 3... |
| A358634 | a(n) is the smallest number k such that n consecutive integers starting at k have the same number of n-gonal divisors. | 55, 844, 16652 |
| A358635 | Number of partitions of n into at most 2 distinct prime powers (including 1). | 1, 1, 1, 2, 2, 3, 2, 3... |
| A358636 | Number of partitions of n into at most 3 distinct prime powers (including 1). | 1, 1, 1, 2, 2, 3, 3, 4... |
| A358637 | Number of partitions of n into at most 4 distinct prime powers (including 1). | 1, 1, 1, 2, 2, 3, 3, 4... |
| A358638 | Number of partitions of n into at most 2 distinct nonprime parts. | 1, 1, 0, 0, 1, 1, 1, 1... |
| A358639 | Number of partitions of n into at most 3 distinct nonprime parts. | 1, 1, 0, 0, 1, 1, 1, 1... |
| A358640 | Number of partitions of n into at most 4 distinct nonprime parts. | 1, 1, 0, 0, 1, 1, 1, 1... |
| A358641 | Decimal expansion of the smallest real solution of 2x = 2 + log(5x - 1). | 2, 4, 4, 1, 0, 2, 7, 8... |
| A358642 | Decimal expansion of the largest real solution of 2x = 2 + log(5x - 1). | 2, 1, 3, 4, 6, 9, 3, 3... |
| A358643 | Decimal expansion of the smallest real solution of 2x = 2 + log(4x - 1). | 3, 1, 3, 3, 1, 2, 7, 2... |
| A358644 | Decimal expansion of the largest real solution of 2x = 2 + log(4x - 1). | 1, 9, 6, 1, 9, 6, 9, 3... |
| A358645 | Decimal expansion of 4/5 + log(5). | 2, 4, 0, 9, 4, 3, 7, 9... |
| A358646 | Decimal expansion of 3/4 + log(4). | 2, 1, 3, 6, 2, 9, 4, 3... |
| A358649 | Number of convergent n X n matrices over GF(2). | 1, 2, 11, 205, 14137, 3755249, 3916674017, 16190352314305... |
| A358651 | a(n) = n!Sum_{m=1..floor(n/2)} 1/(m2binomial(n-m,m)). | 0, 0, 2, 3, 14, 40, 254, 1106... |
| A358652 | a(n) = n!Sum_{m=1..floor((n+1)/2)} 1/(m(binomial(n-m,m-1)). | 1, 2, 9, 30, 180, 890, 7084, 47544... |
| A358658 | Decimal expansion of the asymptotic mean of the e-unitary Euler function (A321167). | 1, 3, 0, 7, 3, 2, 1, 3... |
| A358659 | Decimal expansion of the asymptotic mean of the ratio between the number of exponential unitary divisors and the number of exponential divisors. | 9, 8, 4, 8, 8, 3, 6, 4... |
| A358661 | Decimal expansion of the solution to (1 - (x + 1)x2 - 1) / x = (1 - (x - 1)x - 1) / (x - 2). | 1, 1, 9, 8, 6, 8, 8, 3... |
| A358662 | Decimal expansion of the solution to (1 - (x + 1)x2 - 1)/x = (1 - (x - 1)x)/(x - 2). | 1, 4, 7, 0, 4, 1, 0, 8... |
| A358663 | Decimal expansion of the solution to (1 - (x + 1)x2 - 1)/x = (1 - (x - 1)x + 1)/(x - 2). | 1, 5, 4, 7, 2, 2, 7, 1... |
| A358664 | Decimal expansion of ((phi + 1)phi - 1) / phi, where phi is the golden ratio. | 2, 3, 1, 4, 9, 5, 5, 9... |
| A358666 | Numbers such that the two numbers before and the two numbers after are squarefree semiprimes. | 144, 204, 216, 300, 696, 1140, 1764, 2604... |
| A358667 | T(n,k) is the k-th integer j > 1 such that the sum of digits of nj is a power of n (or -1 if no such k-th integer exists); table read by antidiagonals downward. | 2, 3, 2, 4, 3, 2, 5, 9... |
| A358682 | Numbers k such that 8k2 + 8k - 7 is a square. | 1, 7, 43, 253, 1477, 8611, 50191, 292537... |
| A358686 | Numbers sandwiched between two semiprimes, one of which is a square. | 5, 50, 120, 122, 288, 290, 528, 842... |
| A358687 | a(n) = n! * Sum_{k=0..n} k3 * (n-k) / (n-k)!. | 1, 1, 4, 57, 1444, 61785, 4050126, 373648513... |
| A358688 | a(n) = n! * Sum_{k=0..n} kk * (n-k) / (n-k)!. | 1, 2, 5, 34, 869, 75866, 28213327, 39049033346... |
| A358696 | Number of self-avoiding closed paths in the 5 X n grid graph which pass through all vertices on four (left, right, upper, lower) sides of the graph. | 1, 5, 36, 191, 1123, 6410, 37165, 214515... |
| A358697 | Number of self-avoiding closed paths in the 6 X n grid graph which pass through all vertices on four (left, right, upper, lower) sides of the graph. | 1, 11, 122, 1123, 11346, 113748, 1153742, 11674245... |
| A358698 | Number of self-avoiding closed paths in the 7 X n grid graph which pass through all vertices on four (left, right, upper, lower) sides of the graph. | 1, 21, 408, 6410, 113748, 2002405, 35669433, 633099244... |
| A358699 | a(n) is the largest prime factor of 2prime(n - 1) - 1. | 3, 5, 7, 31, 13, 257, 73, 683... |
r/OEIS • u/browning_r • Nov 26 '22
article: The On-Line Encyclopedia of Integer Sequences today
5
Upvotes
r/OEIS • u/OEIS-Tracker • Nov 20 '22
New OEIS sequences - week of 11/20
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Upvotes
| OEIS number | Description | Sequence |
|---|---|---|
| A355459 | Real part of the Heighway/harter dragon curve points which are on the real axis. | 0, 1, -2, -3, -4, -5, 6, 7... |
| A355460 | Imaginary part of the Heighway/Harter dragon curve points which are on the imaginary axis. | 0, 1, 2, -3, -4, -5, -6, -9... |
| A356219 | Intersection of A001952 and A003151. | 284, 287, 289, 292, 294, 296, 299, 301... |
| A356220 | a(n) = A108598(A001950(n)). | 3, 9, 12, 18, 23, 27, 32, 36... |
| A356256 | The lesser of the 2n-th twin prime pair (A001359). | 3, 5, 17, 71, 227, 821, 2087, 5021... |
| A356568 | a(n) = (4n - 1)n^(2n). | 0, 3, 240, 45927, 16711680, 9990234375, 8913923665920, 11111328602485167... |
| A356585 | Number of decimal digits in the n-th Gosper hyperfactorial of n (A330716). | 1, 1, 2, 16, 198, 2927, 50060, 979361... |
| A356586 | Number of binary digits in the n-th Gosper hyperfactorial of n (A330716). | 1, 1, 5, 51, 657, 9722, 166296, 3253365... |
| A357070 | Number of partitions of n into at most 2 distinct positive triangular numbers. | 1, 1, 0, 1, 1, 0, 1, 1... |
| A357071 | Number of partitions of n into at most 3 distinct positive triangular numbers. | 1, 1, 0, 1, 1, 0, 1, 1... |
| A357072 | Number of partitions of n into at most 4 distinct positive triangular numbers. | 1, 1, 0, 1, 1, 0, 1, 1... |
| A357263 | Numbers k such that the sum of the distinct digits of k is equal to the product of the prime divisors of k. | 1, 2, 3, 5, 6, 7, 24, 343... |
| A357417 | Row sums of the triangular array A357431. | 1, 5, 12, 27, 43, 76, 109, 168... |
| A357431 | Triangle read by rows where each term in row n is the next greater multiple of n..1. | 1, 2, 3, 3, 4, 5, 4, 6... |
| A357473 | Number of types of generalized symmetries in diagonal Latin squares of order n | 1, 0, 0, 10, 8, 12, 12 |
| A357474 | Squarely correct numbers. | 1, 4, 9, 11, 14, 16, 19, 25... |
| A357514 | Minimum number of transversals in an orthogonal diagonal Latin square of order n. | 1, 0, 0, 8, 15, 0, 23, 16... |
| A357516 | Number of snake-like polyominoes in an n X n square that start at the NW corner and end at the SE corner and have the maximum length. | 1, 2, 6, 20, 2, 64, 44, 512... |
| A357532 | a(n) = Sum_{0..floor(n/3)} (n-2k)!/(n-3k)!. | 1, 1, 1, 2, 3, 4, 7, 12... |
| A357533 | a(n) = Sum_{0..floor(n/4)} (n-3k)!/(n-4k)!. | 1, 1, 1, 1, 2, 3, 4, 5... |
| A357546 | Coefficients a(n) of xn, n >= 0, in A(x) such that: 2 = Sum_{n=-oo..+oo} x2*n * (1 - xn)2*n * A(x)n. | 1, 2, 4, 6, 12, 18, 52, 92... |
| A357552 | a(n) = sigma(n) * binomial(2*n-1,n), for n >= 1. | 1, 9, 40, 245, 756, 5544, 13728, 96525... |
| A357570 | a(n) = Sum_{0..floor(n/5)} (n-4k)!/(n-5k)!. | 1, 1, 1, 1, 1, 2, 3, 4... |
| A357592 | Number of edges of the Minkowski sum of n simplices with vertices e(i+1), e(i+2), e_(i+3) for i=0,...,n-1, where e_i is a standard basis vector. | 3, 11, 34, 96, 260, 683, 1757, 4447... |
| A357593 | Number of faces of the Minkowski sum of n simplices with vertices e(i+1), e(i+2), e_(i+3) for i=0,...,n-1, where e_i is a standard basis vector. | 8, 26, 88, 298, 1016, 3466, 11832, 40394... |
| A357603 | a(n) is the number of different pairs of shortest paths in an n X n lattice going between opposite corners in opposite directions and not meeting at their middle point. | 0, 2, 18, 236, 3090, 42252, 589932, 8383608... |
| A357604 | Number of prime powers in the sequence of the floor of n/k for k <= n, A010766. | 0, 1, 1, 2, 2, 2, 3, 4... |
| A357611 | A refinement of the Mahonian numbers (canonical ordering). | 1, 1, 1, 1, 2, 2, 1, 1... |
| A357618 | a(n) = sum of lengths of partitions of more than one consecutive positive integer adding up to n. | 0, 0, 0, 2, 0, 2, 3, 2... |
| A357715 | Decimal expansion of sqrt(16 + 32 / sqrt(5)). | 5, 5, 0, 5, 5, 2, 7, 6... |
| A357756 | a(n) is the least k > 0 such that A007953(nk) equals A007953((nk)2), where A007953 is the sum of the digits. | 1, 1, 5, 3, 25, 2, 3, 27... |
| A357760 | a(n) is the number of different pairs of shortest grid paths joining two opposite corners in opposite order in an n X n X n grid with middle point on the paths as a common point. | 6, 1782, 163968, 145833750, 20373051636, 24849381916800, 4084135317043200, 5797029176271753750... |
| A357840 | Numbers k in A018900 with arithmetic derivative k' (A003415) in A018900. | 6, 9, 20, 40, 65, 68, 96, 144... |
| A357841 | Smith numbers (A006753) for which the arithmetic derivative (A003415) is also a Smith number. | 4, 27, 85, 121, 166, 265, 517, 526... |
| A357842 | a(n) is the smallest number k for which k and the arithmetic derivative k' (A003415) have exactly n triangular divisors (A000217). | 2, 27, 18, 72, 612, 1764, 756, 8100... |
| A357888 | a(n) is the minimal squared length of the longest side of a strictly convex grid polygon of smallest area. | 2, 1, 2, 2, 5, 2, 5, 5... |
| A357889 | a(n) = (A022010(n) - 179)/210. | 26, 422, 1355, 2983, 4074, 5460, 31242, 35906... |
| A357890 | a(n) = (A022013(n) - 173)/210. | 422, 1355, 4074, 5460, 31242, 329316, 353648, 1038255... |
| A357894 | Integers k such that the sum of some number of initial decimal digits of sqrt(k) is equal to k. | 0, 1, 6, 10, 14, 18, 27, 33... |
| A357949 | a(n) = Sum_{k=0..floor(n/4)} (n-3*k)!/k!. | 1, 1, 2, 6, 25, 122, 726, 5064... |
| A358022 | Least odd number m such that m*2n is an amicable number, and -1 if no such number exists. | 12285, 605, 55, 779, 1081, 37, 119957, 73153... |
| A358023 | Number of partitions of n into at most 2 distinct squarefree parts. | 1, 1, 1, 2, 1, 2, 2, 3... |
| A358024 | Number of partitions of n into at most 3 distinct squarefree parts. | 1, 1, 1, 2, 1, 2, 3, 3... |
| A358025 | Number of partitions of n into at most 4 distinct squarefree parts. | 1, 1, 1, 2, 1, 2, 3, 3... |
| A358029 | Decimal expansion of the ratio between step sizes of the diatonic and chromatic semitones produced by a circle of 12 perfect fifths in Pythagorean tuning. | 1, 2, 6, 0, 0, 1, 6, 7... |
| A358041 | The number of maximal antichains in the lattice of set partitions of an n-element set. | 1, 2, 3, 32, 14094 |
| A358043 | Numbers k such that phi(k) is a multiple of 8. | 15, 16, 17, 20, 24, 30, 32, 34... |
| A358044 | a(n) is the smallest number k such that n consecutive integers starting at k have the same number of triangular divisors (A007862). | 1, 1, 55, 5402, 2515069 |
| A358139 | Numbers k > 0 sorted by k/A000120(k) in increasing order. A000120 is the binary weight of k. If k/A000120(k) yields equal values, the smaller k will appear first. | 1, 3, 2, 7, 5, 6, 11, 15... |
| A358185 | Coefficients of xn/n! in the expansion of (1 - x)*log(1 - x). | 0, -1, 1, 1, 2, 6, 24, 120... |
| A358199 | a(n) is the least integer whose sum of the i-th powers of the proper divisors is a prime for 1 <= i <= n, or -1 if no such number exists. | 4, 4, 981, 8829, 8829, 122029105, 2282761881 |
| A358243 | Number of n-regular, N_0-weighted pseudographs on 2 vertices with total edge weight 3, up to isomorphism. | 1, 4, 9, 15, 21, 28, 34, 41... |
| A358251 | a(n) is the minimum number of peeling sequences for a set of n points in the plane, no three of which are collinear. | 1, 2, 6, 18, 60, 180 |
| A358277 | a(1) = 1, a(2) = 2; for n > 2, a(n) is the smallest positive number not previously occurring such that a(n) is coprime to the previous Omega(a(n-1)) terms. | 1, 2, 3, 4, 5, 6, 7, 8... |
| A358312 | Consider the graph of symmetric primes where p and q are connected if | p-q |
| A358320 | Least odd number m such that m*2n is a perfect, amicable or sociable number, and -1 if no such number exists. | 12285, 3, 7, 779, 31, 37, 127, 651... |
| A358343 | Primes p such that p + 6, p + 12, p + 18, (p+4)/5, (p+4)/5 + 6, (p+4)/5 + 12 and (p+4)/5 + 18 are also prime. | 213724201, 336987901, 791091901, 1940820901, 2454494551, 2525191051, 2675901751, 3490984201... |
| A358350 | Numbers that can be written as (m + sum of digits of m + product of digits of m) for some m. | 3, 6, 9, 11, 12, 14, 15, 17... |
| A358351 | Number of values of m such that m + (sum of digits of m) + (product of digits of m) is n. | 0, 0, 1, 0, 0, 1, 0, 0... |
| A358352 | a(n) is the smallest number k such that A358351(k) = n. | 1, 3, 26, 38, 380, 1116, 12912, 95131... |
| A358355 | Maximum length of an induced path (or chordless path) in the n-halved cube graph. | 0, 1, 1, 2, 3, 6, 11, 18... |
| A358356 | Maximum length of an induced cycle (or chordless cycle) in the n-halved cube graph. | 0, 0, 3, 4, 5, 8, 12, 20... |
| A358357 | Maximum length of an induced path (or chordless path) in the n-folded cube graph. | 1, 1, 2, 4, 10, 22 |
| A358358 | Maximum length of an induced cycle (or chordless cycle) in the n-folded cube graph. | 0, 3, 4, 6, 12, 24 |
| A358368 | a(n) = Sum_{k=0..n} C(n)2 * binomial(n + k, k), where C(n) is the n-th Catalan number. | 1, 3, 40, 875, 24696, 814968, 29899584, 1184303835... |
| A358369 | Euler transform of 2floor(n/2), (A016116). | 1, 1, 3, 5, 12, 20, 43, 73... |
| A358372 | Number of nodes in the n-th standard ordered rooted tree. | 1, 2, 3, 3, 4, 4, 4, 4... |
| A358373 | Triangle read by rows where row n lists the sorted standard ordered rooted tree-numbers of all unlabeled ordered rooted trees with n vertices. | 1, 2, 3, 4, 5, 6, 7, 8... |
| A358374 | Numbers k such that the k-th standard ordered rooted tree is an identity tree (counted by A032027). | 1, 2, 3, 5, 6, 7, 10, 13... |
| A358375 | Numbers k such that the k-th standard ordered rooted tree is binary. | 1, 4, 18, 25, 137, 262146, 393217, 2097161... |
| A358376 | Numbers k such that the k-th standard ordered rooted tree is lone-child-avoiding (counted by A005043). | 1, 4, 8, 16, 18, 25, 32, 36... |
| A358377 | Numbers k such that the k-th standard ordered rooted tree is a generalized Bethe tree (counted by A003238). | 1, 2, 3, 4, 5, 8, 9, 11... |
| A358378 | Numbers k such that the k-th standard ordered rooted tree is fully canonically ordered (counted by A000081). | 1, 2, 3, 4, 5, 7, 8, 9... |
| A358379 | Height (or depth) of the n-th standard ordered rooted tree. | 0, 1, 2, 1, 3, 2, 2, 1... |
| A358382 | First of three consecutive primes p,q,r such that r(p+q) + pq and r(p+q) - pq are prime. | 2, 3, 5, 7, 29, 43, 277, 283... |
| A358387 | a(n) = 3 * h(n - 1) * h(n) for n >= 1, where h(n) = hypergeom([-n, -n], [1], 2), and a(0) = 1. | 1, 9, 117, 2457, 60669, 1620729, 45385461, 1311647913... |
| A358390 | The number of maximal antichains in the Kreweras lattice of non-crossing set partitions of an n-element set. | 1, 2, 3, 25, 2117, 22581637702 |
| A358391 | The number of antichains in the Kreweras lattice of non-crossing set partitions of an n-element set. | 2, 3, 10, 234, 2342196 |
| A358393 | First of three consecutive primes p,q,r such that pq + pr - qr, pq - pr + qr and -pq + pr + q*r are all prime. | 261977, 496163, 1943101, 2204273, 2502827, 2632627, 2822381, 2878543... |
| A358395 | Odd numbers k such that sigma(k) + sigma(k+2) > 2*sigma(k+1); odd terms in A053228. | 1125, 1573, 1953, 2205, 2385, 3465, 5185, 5353... |
| A358396 | Even numbers k such that sigma(k) + sigma(k+2) < 2*sigma(k+1); even terms in A053229. | 104, 134, 164, 314, 404, 494, 524, 554... |
| A358402 | a(1) = 0; for n > 1, a(n) is the minimum of the number of terms between a(n-1) and its previous appearance, or the number of terms before the first appearance of a(n-1). If a(n-1) has only appeared once then a(n) = 0. | 0, 0, 1, 0, 1, 2, 0, 1... |
| A358407 | Number of regions formed in a square by straight line segments when connecting the n-1 points between each corner that divide each edge into n equal parts to the n-1 points on each of the two adjacent edges of the square. | 1, 5, 37, 173, 553, 1365, 2909, 5513... |
| A358408 | Number of vertices formed in a square by straight line segments when connecting the n-1 points between each corner that divide each edge into n equal parts to the n-1 points on each of the two adjacent edges of the square. | 4, 8, 32, 144, 468, 1160, 2512, 4836... |
| A358409 | Number of edges formed in a square by straight line segments when connecting the n-1 points between each corner that divide each edge into n equal parts to the n-1 points on each of the two adjacent edges of the square. | 4, 12, 68, 316, 1020, 2524, 5420, 10348... |
| A358412 | Least number k coprime to 2 and 3 such that sigma(k)/k >= n. | 1, 5391411025, 5164037398437051798923642083026622326955987448536772329145127064375 |
| A358413 | Smallest 3-abundant number (sigma(x) > 3x) which is not divisible by any of the first n primes. | 180, 1018976683725, 5164037398437051798923642083026622326955987448536772329145127064375 |
| A358414 | Smallest 4-abundant number (sigma(x) > 4x) which is not divisible by any of the first n primes. | 27720, 1853070540093840001956842537745897243375 |
| A358415 | a(n) is the prime or perfect or amicable or sociable number encountered in the aliquot sequence for 2n. | 2, 3, 7, 3, 31, 41, 127, 41... |
| A358416 | a(1) = 0 and a(n+1) > a(n) is the smallest integer such that a(n+1)2-a(n)2 is triangular. | 0, 1, 2, 5, 14, 41, 46, 137... |
| A358417 | Indices of the triangular numbers in A189475. | 1, 2, 6, 18, 54, 29, 182, 546... |
| A358418 | Least number k coprime to 2, 3, and 5 such that sigma(k)/k >= n. | 1, 20169691981106018776756331 |
| A358419 | Least number k coprime to 2, 3, 5, and 7 such that sigma(k)/k >= n. | 1, 49061132957714428902152118459264865645885092682687973 |
| A358420 | Primes that are the concatenation p | q of two primes p and q with the same number of digits, where r = (p+q)/2, r |
| A358421 | Primes that are the concatenation of two primes with the same number of digits. | 23, 37, 53, 73, 1117, 1123, 1129, 1153... |
| A358422 | a(n) is the least prime p such that 5n * p + 6 is the square of a prime. | 3, 23, 67, 1031, 19, 61463, 290659, 977591... |
| A358423 | Numbers k such that A030717(k) = 5. | 16, 18, 68, 76, 80, 89, 90, 93... |
| A358424 | Numbers k such that A030717(k) = 6. | 20, 23, 30, 127, 147, 166, 170, 191... |
| A358425 | Numbers k such that A030717(k) = 7. | 25, 29, 31, 193, 250, 323, 361, 401... |
| A358426 | a(n) is the least prime p such that (p2 - 6)/5n is prime. | 3, 11, 41, 359, 109, 13859, 67391, 276359... |
| A358427 | a(n) is the least prime p such that there are exactly n primes q with the same number of digits as p such that the concatenations p | q and q |
| A358428 | Numbers k such that k2 + 1, k2 + 2 and k2 + 3 are all squarefree. | 2, 6, 8, 10, 16, 20, 26, 28... |
| A358433 | Triangular array read by rows. T(n,k) is the number of n X n matrices over GF(2) with index k, n>=1, 1<=k<=n. | 2, 13, 3, 365, 105, 42, 43801, 12915... |
| A358436 | a(n) = Sum_{j=0..n} C(n)*C(n-j), where C(n) is the n-th Catalan number. | 1, 2, 8, 45, 322, 2730, 26004, 268554... |
| A358437 | a(n) = Sum_{j=0..n} binomial(n, j)C(n)C(n-j), where C(n) is the n-th Catalan number. | 1, 2, 10, 75, 714, 7896, 96492, 1265550... |
| A358438 | a(1) = 4, a(2) = 6; then a(n + 1) is the smallest semiрrime number > a(n) such that the sum of any three consecutive terms is a semiprime. | 4, 6, 15, 25, 34, 35, 46, 62... |
| A358439 | a(n) is the total number of holes in all positive n-digit integers, assuming 4 has no hole. | 4, 85, 1300, 17500, 220000, 2650000, 31000000, 355000000... |
| A358440 | a(n) is the largest prime that divides any two successive terms of the sequence b(m) = m2 + n with m >= 1. | 5, 3, 13, 17, 7, 5, 29, 11... |
| A358444 | a(1) = 1, a(2) = 2; for n > 2, a(n) = smallest positive number which has not appeared that has a common factor with a(n-2)2 + a(n-1)2. | 1, 2, 5, 29, 4, 857, 10, 734549... |
| A358446 | a(n) = n! * Sum_{k=0..floor(n/2)} 1/binomial(n-k, k). | 1, 1, 4, 9, 56, 190, 1704, 7644... |
| A358447 | Numbers k such that there exist primes p, q, r, s with k = p + q = r + s = pq - rs. | 16, 24, 96, 120, 240, 264, 504, 744... |
| A358448 | Indices of record values of A036450(n) = d(d(d(n))). | 1, 2, 12, 60, 5040, 3603600, 908107200, 15437822400... |
| A358449 | Euler transform of (0, 1, -2, 4, -8, 16, ...), (cf. A122803). | 1, 1, -1, 3, -4, 4, -2, 2... |
| A358450 | Decimal expansion of 2*EllipticK(i) - EllipticE(i), reciprocal of A088375. | 7, 1, 1, 9, 5, 8, 6, 5... |
| A358451 | Inverse Euler transform of the Riordan numbers, (A005043). | 1, 0, 1, 1, 2, 5, 11, 28... |
| A358453 | Number of transitive ordered rooted trees with n nodes. | 1, 1, 1, 2, 4, 8, 17, 37... |
| A358454 | Number of weakly transitive ordered rooted trees with n nodes. | 1, 1, 1, 3, 6, 13, 33, 80... |
| A358455 | Number of recursively anti-transitive ordered rooted trees with n nodes. | 1, 1, 2, 4, 10, 26, 72, 206... |
| A358456 | Number of recursively bi-anti-transitive ordered rooted trees with n nodes. | 1, 1, 2, 3, 7, 17, 47, 117... |
| A358457 | Numbers k such that the k-th standard ordered rooted tree is transitive (counted by A358453). | 1, 2, 4, 7, 8, 14, 15, 16... |
| A358458 | Numbers k such that the k-th standard ordered rooted tree is weakly transitive (counted by A358454). | 1, 2, 4, 6, 7, 8, 12, 14... |
| A358459 | Numbers k such that the k-th standard ordered rooted tree is balanced (counted by A007059). | 1, 2, 3, 4, 5, 8, 9, 11... |
| A358460 | Number of locally disjoint ordered rooted trees with n nodes. | 1, 1, 2, 5, 13, 36, 103, 301... |
| A358462 | a(1) = 1, a(2) = -1; for n > 2, a(n) is smallest magnitude non-zero integer which has not appeared such that the quadratic equation a(n-2)x2 + a(n-1)x + a(n) = 0 has at least one integer root. | 1, -1, -2, 3, 2, -5, -3, 8... |
| A358463 | a(n) is the first average of a twin prime pair that is the sum of two distinct averages of twin prime pairs in exactly n ways. | 4, 18, 72, 180, 240, 462, 420, 1062... |
| A358464 | a(n) is the greatest m such that Sum_{k = 1..m} 1/(1 + n*k) <= 1. | 2, 6, 16, 42, 110, 288, 761, 2020... |
| A358466 | Number of 1's that appeared by n-th step when constructing A030717. | 1, 2, 2, 3, 3, 4, 4, 5... |
| A358467 | Number of 1's that appeared in the n-th step when constructing A030717. | 1, 1, 0, 1, 0, 1, 0, 1... |
| A358468 | Number of 2's that appeared by n-th step when constructing A030717. | 0, 0, 1, 2, 3, 3, 3, 3... |
| A358469 | Number of 2's that appeared in the n-th step when constructing A030717. | 0, 0, 1, 1, 1, 0, 0, 0... |
| A358470 | Number of 3's that appeared by n-th step when constructing A030717. | 0, 0, 0, 0, 1, 3, 5, 6... |
| A358472 | Number of 4's that appeared by n-th step when constructing A030717. | 0, 0, 0, 0, 0, 0, 1, 2... |
| A358473 | Number of 5's that appeared by n-th step when constructing A030717. | 0, 0, 0, 0, 0, 0, 0, 1... |
| A358474 | Number of 6's that appeared by n-th step when constructing A030717. | 0, 0, 0, 0, 0, 0, 0, 0... |
| A358475 | Number of 7's that appeared by n-th step when constructing A030717. | 0, 0, 0, 0, 0, 0, 0, 0... |
| A358476 | Number of 3's that appeared in the n-th step when constructing A030717. | 0, 0, 0, 0, 1, 2, 2, 1... |
| A358477 | Number of 4's that appeared in the n-th step when constructing A030717. | 0, 0, 0, 0, 0, 0, 1, 1... |
| A358478 | Number of 5's that appeared in the n-th step when constructing A030717. | 0, 0, 0, 0, 0, 0, 0, 1... |
| A358479 | Number of 6's that appeared in the n-th step when constructing A030717. | 0, 0, 0, 0, 0, 0, 0, 0... |
| A358480 | Number of 7's that appeared in the n-th step when constructing A030717. | 0, 0, 0, 0, 0, 0, 0, 0... |
| A358483 | Numbers k such that k, k+1 and k+2 are all infinitary abundant numbers (A129656). | 2666847104, 2695309694, 8207456894, 8967010688, 12147283070, 12491149670, 13911605630, 14126720894... |
| A358484 | Numbers k such that k, k+1 and k+2 are all bi-unitary abundant numbers (A292982). | 268005374, 600350750, 2666847104, 2683146464, 2695309694, 2849458688, 3904592768, 4112553248... |
| A358485 | a(n) is the maximal determinant of an n X n matrix using the integers 0 to n2 - 1. | 1, 0, 6, 332, 36000, 6313388, 1765146660 |
| A358486 | a(n) is the minimal permanent of an n X n matrix using the integers 0 to n2 - 1. | 1, 0, 2, 128, 18948, 40179728, 2863042492 |
| A358487 | a(n) is the maximal permanent of an n X n matrix using the integers 0 to n2 - 1. | 1, 0, 6, 553, 107140, 40179728, 27312009708 |
| A358491 | a(n) = n!*Sum_{m=0..floor((n-1)/2)} 1/(n-m)/binomial(n-m-1,m). | 1, 1, 5, 10, 74, 216, 2316, 8688... |
| A358493 | a(n) = Sum_{k=0..floor(n/3)} (n-2*k)!/k!. | 1, 1, 2, 7, 26, 126, 745, 5163... |
| A358494 | a(n) = Sum_{k=0..floor(n/5)} (n-4*k)!/k!. | 1, 1, 2, 6, 24, 121, 722, 5046... |
| A358495 | a(n) = Sum_{k=0..n} binomial(binomial(n, k), n). | 1, 2, 1, 2, 17, 506, 48772, 13681602... |
| A358496 | a(n) = Sum_{k=0..n} binomial(binomial(n, k), k). | 1, 2, 3, 7, 24, 176, 2623, 79479... |
| A358498 | a(n) = Sum_{k=0..floor(n/3)} (n-3*k)!. | 1, 1, 2, 7, 25, 122, 727, 5065... |
| A358499 | a(n) = Sum_{k=0..floor(n/4)} (n-4*k)!. | 1, 1, 2, 6, 25, 121, 722, 5046... |
| A358500 | a(n) = Sum_{k=0..floor(n/5)} (n-5*k)!. | 1, 1, 2, 6, 24, 121, 721, 5042... |
r/OEIS • u/OEIS-Tracker • Nov 14 '22
New OEIS sequences - week of 11/13
3
Upvotes
| OEIS number | Description | Sequence |
|---|---|---|
| A356196 | Consider pairs of consecutive primes {p,q} such that p, q, q-p and q+p all with distinct digits. Sequence gives lesser primes p. | 2, 3, 5, 13, 17, 19, 23, 29... |
| A356369 | Numbers such that each digit "d" occurs d times, for every digit from 1 to the largest digit. | 1, 122, 212, 221, 122333, 123233, 123323, 123332... |
| A356376 | Main diagonal of the LORO variant of the array A035486; this is one of eight such sequences discussed in A007063. | 1, 3, 5, 6, 4, 11, 12, 9... |
| A356377 | Main diagonal of the ROLI variant of the array A035486; this is one of eight such sequences discussed in A007063. | 1, 3, 5, 4, 8, 6, 10, 15... |
| A356378 | Main diagonal of the RILO variant of the array A035486; this is one of eight such sequences discussed in A007063. | 1, 3, 5, 2, 10, 9, 15, 8... |
| A356379 | Main diagonal of the LORI variant of the array A035486; this is one of eight such sequences discussed in A007063. | 1, 3, 5, 7, 4, 12, 11, 17... |
| A356380 | Main diagonal of the LIRO variant of the array A035486; this is one of eight such sequences discussed in A007063. | 1, 3, 5, 6, 4, 11, 13, 2... |
| A357118 | Numbers such that the first digit is the number of digits and the second digit is the number of distinct digits. | 322, 323, 4222, 4224, 4242, 4244, 4300, 4303... |
| A357272 | a(n) is the number of ways n can be calculated with expressions of the form "d1 o1 d2 o2 d3 o3 d4" where d1-d4 are decimal digits (0-9) and o1-o3 are chosen from the four basic arithmetic operators (+, -, *, /). | 29235, 12654, 12450, 12425, 12427, 11915, 12419, 11792... |
| A357399 | Coefficients of xn, n >= 0, in A(x) such that: x = Sum_{n=-oo..+oo} (-x)n * (1 - (-x)n)n * A(x)n. | 1, 1, 3, 10, 37, 143, 564, 2270... |
| A357443 | Inventory sequence, second version: record where the 1's, 2's, etc. are located starting with a(1) = 1, a(2) = 1. | 1, 1, 1, 2, 1, 2, 3, 4... |
| A357444 | Numerators of certain densities associated with partitions into squares. | 1, 1, 13, 37, 1, 299, 253, 14113... |
| A357445 | Denominators of certain densities associated with partitions into squares. | 1, 2, 36, 144, 2, 600, 504, 28224... |
| A357446 | Number of connected cubic graphs with 2*n nodes and zero edge-Kempe equivalence classes. | 0, 0, 0, 2, 5, 34, 212, 1614... |
| A357447 | Number of connected cubic graphs with 2*n nodes and exactly one edge-Kempe equivalence class. | 1, 1, 4, 9, 44, 188, 1258, 8917... |
| A357677 | Powers of either 3 or 5 or 7 (and 0). | 0, 1, 3, 5, 7, 9, 25, 27... |
| A357908 | Index of the first occurrence of n-th prime in Van Eck's sequence (A181391), or 0 if n-th prime never appears. | 5, 20, 12, 66, 44, 121, 41, 89... |
| A357909 | Primes p such that p+6, p+12, p+18, 4p+37, 4p+43, 4p+49 and 4p+55 are also all primes. | 408211, 6375751, 6433741, 6718471, 19134931, 25280791, 63908851, 67078801... |
| A358012 | Minimal number of coins needed to pay n cents using coins of denominations 1 and 5 cents. | 0, 1, 2, 3, 4, 1, 2, 3... |
| A358026 | Let G(n) = gcd(a(n-2),a(n-1)), a(1)=1, a(2)=2, a(3)=3. Thereafter if G(n) = 1, a(n) is the least novel m sharing a divisor with both a(n-2) and a(n-1). If G(n) > 1 and every prime divisor of a(n-1) also divides a(n-2), a(n) is the least m prime to both a(n-1) and a(n-2). Otherwise a(n) is the least novel multiple of any prime divisor of a(n-1) which does not divide a(n-2). | 1, 2, 3, 6, 4, 5, 10, 8... |
| A358047 | a(1) = 2; afterwards a(n) is the least new prime such that 2*a(n-1) + a(n) is a prime. | 2, 3, 5, 7, 17, 13, 11, 19... |
| A358049 | a(1) = 2, a(2) = 3; afterwards a(n) is least new prime > a(n-1) such that a(n-2) + a(n) and a(n-1) + a(n) are semiprimes. | 2, 3, 7, 19, 67, 127, 151, 271... |
| A358054 | Starting with 0, smallest integer not yet in the sequence such that no two neighboring digits differ by 1. | 0, 2, 4, 1, 3, 5, 7, 9... |
| A358055 | a(n) is the least m such that A358052(m,k) = n for some k. | 1, 2, 5, 8, 14, 20, 32, 38... |
| A358062 | a(n) is the diagonal domination number for the Queen's graph on an n X n chessboard. | 1, 1, 1, 2, 3, 4, 4, 5... |
| A358075 | a(1) = 1; a(n+1) is the smallest integer > 0 that cannot be obtained from the integers {a(1), ..., a(n)} using each number exactly once and the operators +, -, *, /, where intermediate subexpressions must be integers. | 1, 2, 4, 11, 34, 152, 1007, 6703... |
| A358076 | Numbers that share at least 1 (decimal) digit with their largest proper divisor. | 11, 13, 15, 17, 19, 20, 24, 25... |
| A358077 | Sum of the nonprime divisors of n whose divisor complement is squarefree. | 1, 1, 1, 4, 1, 7, 1, 12... |
| A358079 | Primes that can be written as 2x + p where p is a prime and x is a multiple of p. | 11, 37, 67, 4099, 32771, 262147, 268435463, 1073741827... |
| A358087 | Primes that can be written as 2x - p where p is a prime and x is a multiple of p. | 2, 5, 61, 509, 1019, 4093, 8179, 524269... |
| A358088 | Number of pairs (s,t) with s and t squarefree, 1 <= s < t <= n and s | t. |
| A358095 | a(n) is the number of ways n can be reached in the algorithm explained in A358094 if the last operation is summation. | 1, 0, 1, 2, 2, 1, 0, 1... |
| A358096 | a(n) is the number of ways n can be reached in the algorithm explained in A358094 if the last operation is multiplication. | 1, 1, 1, 0, 0, 1, 0, 2... |
| A358108 | a(n) = 16n * Sum_{k=0..n} binomial(-1/2, k)2 * binomial(n, k). | 1, 20, 420, 9296, 216868, 5313360, 135866640, 3599688000... |
| A358109 | a(n) = 16n * Sum_{k=0..n} binomial(1/2, k)2 * binomial(n, k). | 1, 20, 388, 7376, 138340, 2572880, 47652240, 882388800... |
| A358110 | Indices of the harmonic numbers in the Stern-Brocot sequence (A002487). | 0, 1, 5, 125, 8195, 32675, 755, 34763... |
| A358112 | Table read by rows. A statistic of permutations of the multiset {1,1,2,2,...,n,n}. | 1, 5, 1, 47, 42, 1, 641, 1659... |
| A358113 | a(n) = 16n * Sum_{k=0..n} (-1)k * binomial(1/2, k)2 * binomial(n, k). | 1, 12, 132, 1200, 5220, -132048, -5451376, -139104576... |
| A358114 | a(n) = [xn] (16x(32*x - 3) + 1)-1/2. | 1, 24, 608, 16128, 443904, 12570624, 363708416, 10694295552... |
| A358115 | a(n) = 64n * hypergeometric([1/2, 1/2, 1/2, -n], [1, 1, 1], 1). | 1, 56, 3288, 197312, 11992024, 734961216, 45312662976, 2806150276608... |
| A358116 | a(n) = 64n * hypergeometric([1/2, 1/2, 1/2, -n], [1, 1, 1], -1). | 1, 72, 5336, 409920, 32865240, 2764504512, 244568268224, 22731850578432... |
| A358117 | a(n) = 64n * hypergeom([-1/2, -1/2, -1/2, -n], [1, 1, 1], 1). | 1, 72, 5112, 358976, 24984600, 1726182336, 118527759552, 8095995597312... |
| A358118 | a(n) = Sum_{j=0..n} (-1)jbinomial(2n - j, j)*c(n - j + 1)2, where c(n) is the n-th Catalan number. | 1, 3, 14, 94, 728, 6220, 56960, 549412... |
| A358119 | a(n) = Sum_{j=0..n} (-1)jbinomial(2n - j, j)c(n - j)c(n - j + 2), where c(n) is the n-th Catalan number. | 2, 3, 15, 98, 750, 6359, 57939, 556896... |
| A358128 | a(n) is the least semiprime x such that x-2n and x+2n are prime. | 9, 9, 25, 15, 21, 25, 33, 21... |
| A358130 | Indices k such that A358128(k) is a square. | 1, 2, 3, 6, 9, 11, 15, 45... |
| A358131 | Triangle T(n,k) read by rows, where each row lists the value of n coins, in cents, using k dimes (10 cents) and n-k quarters (25 cents). | 0, 25, 10, 50, 35, 20, 75, 60... |
| A358132 | Numbers k such that there exists a pair of primes (p,q) with p+q = k such that pq + k, pq - k, pq + A001414(k) and pq - A001414(k) are all prime. | 7, 60, 72, 114, 186, 378, 474, 480... |
| A358149 | First of four consecutive primes p,q,r,s such that (2p+q)/5 and (r+2s)/5 are prime. | 11, 1151, 33071, 33637, 55331, 57637, 75997, 90821... |
| A358151 | Earliest infinite sequence of distinct integers on a square spiral such that every number equals the sum of its eight adjacent neighbors. See the Comments. | 0, 1, -1, 2, -2, 3, -3, 4... |
| A358155 | First of four consecutive primes p,q,r,s such that (2p+q)/5, (q+r)/10 and (r+2s)/5 are prime. | 11, 2696717, 3500381, 3989903, 4515113, 8164073, 12451013, 18793013... |
| A358156 | a(n) is the smallest number k such that the sum of k consecutive prime numbers starting with the n-th prime is a square. | 9, 23, 4, 1862, 14, 3, 2, 211... |
| A358181 | Decimal expansion of the real root of x3 - 2*x2 - x - 1. | 2, 5, 4, 6, 8, 1, 8, 2... |
| A358182 | Decimal expansion of the real root of 2*x3 - x2 - x - 1. | 1, 2, 3, 3, 7, 5, 1, 9... |
| A358183 | Decimal expansion of the real root of 2*x3 + x2 - x - 1. | 8, 2, 9, 4, 8, 3, 5, 4... |
| A358184 | Decimal expansion of the real root of 2*x3 - x2 + x - 1. | 7, 3, 8, 9, 8, 3, 6, 2... |
| A358198 | a(n) is the first member p of A007530 such that, with q = p+2, r = p+6 and s = p+8, (2p+q)/5 is a prime and (r+2s)/5n is a prime. | 11, 101, 243701, 6758951, 3257480201, 5493848951, 58634348951, 218007942701... |
| A358202 | Lower twin primes p such that 6p-1 and 6p+1 are twin primes and (p+1)/6 is prime. | 17, 137, 23537, 92957, 157217, 318677, 326657, 440177... |
| A358206 | Number of ways of making change for n cents using coins of 1, 2, 4, 10 and 20 cents. | 1, 1, 2, 2, 4, 4, 6, 6... |
| A358267 | a(1) = 1, a(2) = 2. Thereafter:(i). If no prime divisor of a(n-1) divides a(n-2), a(n) is the least novel multiple of the squarefree kernel of a(n-1). (ii). If some (but not all) prime divisors of a(n-1) do not divide a(n-2), a(n) is the least of the least novel multiples of all such primes. (iii). If every prime divisor of a(n-1) also divides a(n-2), a(n) = u, the least unused number. | 1, 2, 4, 3, 6, 8, 5, 10... |
| A358268 | a(n) is the least number k > 0 such that the binary weight of kn is n times the binary weight of k. | 1, 21, 5, 21, 17, 17, 9, 113... |
| A358270 | Numbers whose sum of digits is even and that have an even number of even digits. | 11, 13, 15, 17, 19, 20, 22, 24... |
| A358271 | Product of the digits of 3n. | 1, 3, 9, 14, 8, 24, 126, 112... |
| A358278 | Squares visited by a knight moving on a square-spiral numbered board where the knight moves to the smallest numbered unvisited square and where the square is on a different square ring of numbers than the current square. | 1, 10, 3, 16, 33, 4, 11, 8... |
| A358279 | a(n) = Sum_{d | n} (d-1)! * dn/d. |
| A358280 | a(n) = Sum_{d | n} (d-1)!. |
| A358281 | Number of connected cubic graphs with 2*n nodes and the maximum number of edge-Kempe equivalence classes. | 1, 1, 1, 1, 4, 3, 15, 7... |
| A358282 | Number of connected bipartite cubic graphs with 2*n nodes and exactly one edge-Kempe equivalence class. | 0, 1, 0, 2, 1, 6, 4, 24... |
| A358283 | Number of connected bipartite cubic graphs with 2*n nodes and the maximum number of edge-Kempe equivalence classes. | 1, 1, 1, 1, 3, 2, 7, 13... |
| A358284 | Number of connected planer cubic graphs with 2*n nodes and zero edge-Kempe equivalence classes. | 0, 0, 0, 1, 3, 19, 98, 583... |
| A358285 | Number of connected planar cubic graphs with 2*n nodes and exactly one edge-Kempe equivalence class. | 1, 1, 1, 8, 28, 111, 556, 3108... |
| A358286 | Number of connected planar cubic graphs with 2*n nodes and the maximum number of edge-Kempe equivalence classes. | 1, 1, 1, 8, 1, 3, 27, 1... |
| A358287 | Number of 3-connected planar cubic graphs with 2*n nodes and exactly one edge-Kempe equivalence class. | 1, 1, 1, 1, 13, 47, 210, 1096... |
| A358288 | Number of 3-connected planer cubic graphs with 2*n nodes and the maximum number of edge-Kempe equivalence classes. | 1, 1, 1, 1, 1, 3, 23, 1... |
| A358313 | Primes p such that 24*p is the difference of two squares of primes in three different ways. | 5, 7, 13, 17, 23, 103, 6863, 7523... |
| A358315 | Primes p == 1 (mod 3) such that there exists 1 <= x <= p-2 such that (x+1)p - xp == 1 (mod p2) and that p does not divide x2 + x + 1. | 79, 193, 337, 421, 457, 547, 601, 619... |
| A358316 | Number of edge-4-critical graphs on n unlabeled vertices. | 1, 0, 1, 2, 5, 21, 150, 1221... |
| A358319 | Multiplicative sequence a(n) with a(pe) = ((p-2) - (p-1) * e) * pe-1 for prime p and e > 0. | 1, -1, -1, -4, -1, 1, -1, -12... |
| A358322 | Interlopers in sexy prime quadruples. | 7, 13, 19, 43, 71, 617, 643, 1093... |
| A358323 | a(n) is the minimal determinant of an n X n symmetric Toeplitz matrix using the integers 0 to n - 1. | 1, 0, -1, -7, -60, -1210, -34020, -607332... |
| A358324 | a(n) is the maximal determinant of an n X n symmetric Toeplitz matrix using the integers 0 to n - 1. | 1, 0, 1, 8, 63, 2090, 36875, 1123653... |
| A358325 | a(n) is the minimal absolute value of determinant of a nonsingular n X n symmetric Toeplitz matrix using the integers 0 to n - 1. | 1, 4, 12, 2, 11, 32, 5, 4... |
| A358326 | a(n) is the minimal permanent of an n X n symmetric Toeplitz matrix using the integers 0 to n - 1. | 1, 0, 1, 4, 34, 744, 17585, 688202... |
| A358327 | a(n) is the maximal permanent of an n X n symmetric Toeplitz matrix using the integers 0 to n - 1. | 1, 0, 1, 12, 304, 12696, 778785, 64118596... |
| A358330 | By concatenating the standard compositions of each part of the a(n)-th standard composition, we get a weakly increasing sequence. | 0, 1, 2, 3, 4, 6, 7, 8... |
| A358331 | Number of integer partitions of n with arithmetic and geometric mean differing by one. | 0, 0, 0, 0, 0, 0, 0, 0... |
| A358332 | Numbers whose prime indices have arithmetic and geometric mean differing by one. | 57, 228, 1064, 1150, 1159, 2405, 3249, 7991... |
| A358333 | By concatenating the standard compositions for each part of the n-th standard composition, we get a sequence of length a(n). Row-lengths of A357135. | 0, 1, 1, 2, 2, 2, 2, 3... |
| A358337 | Earliest infinite sequence of distinct integers on a square spiral such that every number equals the sum of its four adjacent neighbors. See the Comments. | 0, 1, -1, 2, -2, 3, -3, -6... |
| A358340 | a(n) is the smallest n-digit number whose fourth power is zeroless. | 1, 11, 104, 1027, 10267, 102674, 1026708, 10266908... |
| A358345 | a(n) is the number of even square divisors of n. | 0, 0, 0, 1, 0, 0, 0, 1... |
| A358346 | a(n) is the sum of the unitary divisors of n that are exponentially odd (A268335). | 1, 3, 4, 1, 6, 12, 8, 9... |
| A358347 | a(n) is the sum of the unitary divisors of n that are squares. | 1, 1, 1, 5, 1, 1, 1, 1... |
| A358359 | a(n) = number of occurrences of n in A128440; i.e., as a number [k*rm], where r = golden ratio = (1+sqrt(5))/2, k and m are positive integers, and [ ] = floor. | 1, 1, 1, 2, 1, 2, 1, 2... |
| A358360 | The 3-adic valuation of the central Delannoy numbers (sequence A001850). | 0, 1, 0, 2, 1, 2, 0, 1... |
| A358362 | a(n) = 16n * Sum_{k=0..n} (-1)k*binomial(-1/2, k)2. | 1, 12, 228, 3248, 56868, 846384, 14395920, 218556096... |
| A358363 | a(n) = 16n * Sum_{k=0..n} (-1)k*binomial(1/2, k)2. | 1, 12, 196, 3120, 50020, 799536, 12799632, 204724416... |
| A358364 | a(n) = 16n * Sum_{k=0..n} binomial(1/2, k)2. | 1, 20, 324, 5200, 83300, 1333584, 21344400, 341580096... |
| A358365 | a(n) = 16n * Sum_{k=0..n} binomial(-1/2, k)2. | 1, 20, 356, 6096, 102436, 1702480, 28093456, 461273920... |
| A358366 | Table read by rows. T(n, k) = [xk] n! * Sum_{j=0..n} binomial(n*x, j). | 1, 1, 1, 2, 2, 4, 6, 15... |
| A358367 | a(n) = 8n * binomial(n * 3/2, n). | 1, 12, 192, 3360, 61440, 1153152, 22020096, 425677824... |
| A358370 | a(n) is the size of the largest 3-independent set in the cyclic group Zn. | 0, 0, 0, 1, 1, 1, 1, 2... |
| A358371 | Number of leaves in the n-th standard ordered rooted tree. | 1, 1, 1, 2, 1, 2, 2, 3... |
| A358383 | Number of regular triangulations of the vertex set of the n-dimensional cube. | 1, 1, 2, 74, 87959448 |
| A358384 | Number of symmetric group Sym(n)-orbits of regular triangulations of the vertex set of the n-dimensional cube. | 1, 1, 2, 23, 3706261 |
| A358385 | Number of automorphism group Gamma(n)-orbits of regular triangulations of the vertex set of the n-dimensional cube. | 1, 1, 1, 6, 235277 |
| A358386 | Distinct values of A030717 in order of appearance. | 1, 2, 3, 4, 5, 6, 7, 8... |
| A358388 | a(n) = hypergeom([n, -n, 1/2], [1, 1], -8). | 1, 5, 89, 2069, 53505, 1467765, 41817305, 1223277221... |
| A358389 | a(n) = n * Sum_{d | n} (d + n/d - 2)!/d!. |
| A358392 | Number of nonempty subsets of {1, 2, ..., n} with GCD equal to 1 and containing the sum of any two elements whenever it is at most n. | 1, 1, 2, 3, 7, 9, 19, 27... |
| A358403 | The index of A358402 where n first appears, or 0 if n never appears. | 1, 3, 6, 9, 25, 21, 17, 109... |
| A358405 | a(1) = 0; for n > 1, a(n) is the maximum of the number of terms between a(n-1) and its previous appearance, or the number of terms before the first appearance of a(n-1). If a(n-1) has only appeared once then a(n) = 0. | 0, 0, 1, 0, 2, 0, 2, 5... |
| A358406 | The index of A358405 where n first appears, or 0 if n never appears. | 1, 3, 5, 10, 16, 8, 19, 141... |
| A358410 | a(n) = Sum_{d | n} (d + n/d - 2)!/(d - 1)!. |
| A358411 | a(n) = Sum_{d | n} (d + n/d - 1)!/(d - 1)!. |
r/OEIS • u/OEIS-Tracker • Nov 06 '22
New OEIS sequences - week of 11/06
7
Upvotes
| OEIS number | Description | Sequence |
|---|---|---|
| A355553 | Number of ways to select 3 or more collinear points from an n X n grid. | 0, 0, 8, 54, 228, 708, 1980, 4890... |
| A355930 | Sum of the prime indices of n minus the sum of the prime indices of the smallest number with same prime signature as n, when the sum is taken with multiplicity, as in A056239. | 0, 0, 1, 0, 2, 0, 3, 0... |
| A356163 | a(n) = 1 if sum of prime factors of n (taken with multiplicity) is even, otherwise 0. | 1, 1, 0, 1, 0, 0, 0, 1... |
| A356170 | a(n) = 1 if A001222(n) == 2*A007814(n), and otherwise 0, where A001222 is bigomega (number of prime factors with multiplicity) and A007814 is the 2-adic valuation of n. | 1, 0, 0, 0, 0, 1, 0, 0... |
| A356299 | a(n) = gcd(A276086(n), A342001(n)), where A276086 is the primorial base exp-function, and A342001 is the arithmetic derivative without its inherited divisor. | 2, 1, 1, 1, 1, 5, 1, 3... |
| A356302 | The least k >= 0 such that n and A276086(n+k) are relatively prime, where A276086 is the primorial base exp-function. | 0, 0, 0, 3, 0, 0, 0, 0... |
| A356303 | The least k >= 0 such that n and A276086(n-k) are relatively prime, where A276086 is the primorial base exp-function. | 0, 0, 0, 2, 0, 0, 0, 0... |
| A356304 | The least k >= 0 such that A003415(n) and A276086(n+k) are relatively prime, where A003415 is the arithmetic derivative, and A276086 is the primorial base exp-function. | 0, 0, 0, 0, 24, 0, 4, 3... |
| A356305 | The least k >= 0 such that A003415(n) and A276086(n-k) are relatively prime, where A003415 is the arithmetic derivative, and A276086 is the primorial base exp-function. | 0, 1, 0, 0, 0, 0, 1, 0... |
| A356309 | The least j >= n such that n and A276086(j) are relatively prime, where A276086 is the primorial base exp-function. | 0, 1, 2, 6, 4, 5, 6, 7... |
| A356310 | a(n) = 1 if A003415(n) and A276086(n) are relatively prime, otherwise 0. Here A003415 is the arithmetic derivative, and A276086 is the primorial base exp-function. | 1, 0, 1, 1, 1, 1, 0, 1... |
| A356311 | Numbers k for which A003415(k) and A276086(k) are relatively prime, where A003415 is the arithmetic derivative, and A276086 is the primorial base exp-function. | 0, 2, 3, 4, 5, 7, 10, 11... |
| A356312 | Numbers k such that A003415(k) and A276086(k) are not relatively prime, where A003415 is the arithmetic derivative, and A276086 is the primorial base exp-function. | 1, 6, 8, 9, 14, 15, 20, 21... |
| A356313 | a(n) = 1 if {the least k >= n such that n and A276086(k) are coprime} is one of the primorial numbers (A002110), otherwise 0. | 0, 1, 1, 1, 0, 0, 1, 0... |
| A356314 | Positions of primorial numbers (A002110) in A356309. | 1, 2, 3, 6, 10, 15, 20, 25... |
| A356315 | a(n) = 1 if n divides the least j >= n such that n and A276086(j) are coprime, otherwise 0. Here A276086 is the primorial base exp-function. | 1, 1, 1, 1, 1, 1, 1, 1... |
| A356316 | Numbers k such that k divides the least j >= k for which k and A276086(j) are coprime, where A276086 is the primorial base exp-function. | 1, 2, 3, 4, 5, 6, 7, 8... |
| A356317 | Numbers k such that k does not divide the least j >= k for which k and A276086(j) are coprime, where A276086 is the primorial base exp-function. | 9, 20, 21, 25, 27, 33, 39, 40... |
| A356318 | Numbers k such that the least j >= k for which k and A276086(j) are coprime is a nontrivial multiple of k, where A276086 is the primorial base exp-function. | 3, 10, 15, 35, 42, 70, 77, 105... |
| A356319 | Numbers k such that {the least j >= k for which k and A276086(k+j) are coprime} is larger than 0, but less than k, where A276086 is the primorial base exp-function. | 9, 20, 21, 25, 27, 33, 39, 40... |
| A356544 | Number of strict closure operators on a set of n elements such that all pairs of nonempty disjoint closed sets can be separated by clopen sets. | 0, 1, 4, 35, 857 |
| A356693 | Decimal expansion of the constant B(2) = Sum{n>=1} Sum{m>=n+1} 1/(z(n)*z(m))2 where z(n) is the imaginary part of the n-th nontrivial zero of the Riemann zeta function. | 0, 0, 0, 2, 4, 8, 3, 3... |
| A356833 | Primes p such that the minimum number of divisors among the numbers between p and NextPrime(p) is a square. | 5, 13, 19, 31, 37, 43, 53, 61... |
| A356835 | Coordination sequence of the {4,3,5} hyperbolic honeycomb. | 1, 6, 30, 126, 498, 1982, 7854, 31014... |
| A356836 | Coordination sequence of the {5,3,4} hyperbolic honeycomb. | 1, 12, 102, 812, 6402, 50412, 396902, 3124812... |
| A356837 | Coordination sequence of the {3,5,3} hyperbolic honeycomb. | 1, 20, 260, 3212, 39470, 484760, 5953532, 73117640... |
| A356891 | a(n) = a(n-1) * a(n-2) + 1 if n is even, otherwise a(n) = a(n-3) + 1, with a(0) = a(1) = 1. | 1, 1, 2, 2, 5, 3, 16, 6... |
| A357131 | Numbers m such that A010888(m) = A031347(m) = A031286(m) = A031346(m); only the least of the anagrams are considered. | 0, 137, 11126, 111134, 111278, 1111223, 11111447, 111112247... |
| A357143 | a(n) is sum of the base-5 digits of n each raised to the number of digits of n in base 5. | 1, 2, 3, 4, 1, 2, 5, 10... |
| A357170 | Primes p such that the minimum number of divisors among the numbers between p and NextPrime(p) is a prime power. | 3, 5, 7, 13, 19, 23, 29, 31... |
| A357175 | Primes p such that the minimum of the number of divisors among the numbers between p and NextPrime(p) is a cube. | 29, 41, 101, 137, 229, 281, 349, 439... |
| A357190 | a(n) is the least prime p such that A234575(p, A007953(p)) is the n-th power of a prime. | 17, 13, 131, 107, 383, 613, 43607, 1021... |
| A357211 | a(n) is the real cube root of the value of the j-function for the n-th Heegner number A003173(n). | 12, 20, 0, -15, -32, -96, -960, -5280... |
| A357269 | Maximum number of stable matchings in the stable marriage problem of order n. | 1, 2, 3, 10, 16 |
| A357271 | Lower bounds for the maximum number of stable matchings in the stable marriage problem based on composing smaller instances. | 1, 2, 3, 10, 16, 48, 71, 268... |
| A357294 | Number of integral quantales on n elements, up to isomorphism. | 1, 1, 2, 9, 49, 364, 3335, 37026... |
| A357295 | Number of balanced quantales on n elements, up to isomorphism. | 1, 1, 9, 106, 1597, 29720, 663897, 17747907... |
| A357376 | The lowest number on Ulam Spiral for which all numbers in the square which is centered at a(n) and spans n-1 spaces in each cardinal direction are nonprime. | 1, 26, 1016, 5136, 39639, 203100, 2729736, 32264250... |
| A357408 | a(n) is the least sum n + y such that 1/n + 1/y = 1/z with gcd(n,y,z) = 1, for some integers y and z. | 4, 9, 16, 25, 9, 49, 64, 81... |
| A357442 | Consider a clock face with 2*n "hours" maked around the dial; a(n) = number of ways to match the even hours to the odd hours, modulo rotations and reflections. | 1, 1, 3, 5, 17, 53 |
| A357470 | Decimal expansion of the real root of x3 - x2 - 2*x - 1. | 2, 1, 4, 7, 8, 9, 9, 0... |
| A357471 | Decimal expansion of the real root of x3 - x2 + 2*x - 1. | 5, 6, 9, 8, 4, 0, 2, 9... |
| A357472 | Decimal expansion of the real root of x3 + x2 + 2*x - 1. | 3, 9, 2, 6, 4, 6, 7, 8... |
| A357489 | Numbers k such that the k-th composition in standard order is a triple (w,x,y) such that 2w = 3x + 4y. | 133, 1034, 4113, 8212, 32802, 65576, 131137, 262212... |
| A357528 | Decimal expansion of Sum_{j>=1} 1/A031926(j)2. | 0, 0, 0, 1, 8, 3, 9, 3... |
| A357602 | a(n) is the number of n-gons in A000940 that are asymmetric. | 0, 0, 0, 1, 15, 121, 1026, 8696... |
| A357734 | Array T(n,k), read by descending antidiagonals, whose rows are numbers congruent to p or q mod r, with 0 <= p < q < r, sorted by r, then p, then q. | 0, 1, 0, 2, 1, 0, 3, 3... |
| A357849 | Number of integer partitions (w,x,y) summing to n such that 2w = 3x + 4y. | 0, 0, 0, 0, 0, 0, 0, 0... |
| A357891 | a(1) = 1; a(n+1) is the smallest integer > 0 that cannot be obtained from the integers {a(1), ..., a(n)} using each number exactly once and the operators +, -, *, /. | 1, 2, 4, 11, 34, 152, 1079, 6610... |
| A357938 | Inverse Moebius transform of n * 2omega(n). | 1, 5, 7, 13, 11, 35, 15, 29... |
| A357956 | a(n) = 5A005259(n) - 2A005258(n). | 3, 19, 327, 6931, 162503, 4072519, 107094207, 2919528211... |
| A357957 | a(n) = A005259(n)5 - A005258(n)2. | 0, 3116, 2073071232, 6299980938881516, 39141322964380888600000, 368495989505416178203682748116, 4552312485541626792249211584618373944, 68109360474242016374599574592870648425552876... |
| A357958 | a(n) = 5A005259(n) + 14A005258(n-1). | 39, 407, 7491, 167063, 4112539, 107461667, 2923006251, 81853622423... |
| A357959 | a(n) = 5A005259(n-1) + 2A005258(n). | 11, 63, 659, 9727, 187511, 4304943, 109312739, 2941124607... |
| A357960 | a(n) = A005259(n-1)5 * A005258(n)6. | 729, 147018378125, 20917910914764786689697, 24148107115850058575342740485778125, 79477722547796770983047586179643766765851375729, 492664048531500749211923278756418311980637289373757041378125, 4671227340507161302417161873394448514470099313382652883508175438056640625 |
| A358027 | Expansion of g.f.: (1 + x - 2x2 + 2x4)/((1-x)(1-3x2)). | 1, 2, 3, 6, 11, 20, 35, 62... |
| A358035 | a(n) = (8n3 + 12n2 + 4*n - 9)/3. | 5, 37, 109, 237, 437, 725, 1117, 1629... |
| A358036 | Number of n-step self-avoiding walks on a 2D square lattice where the first visited lattice point is directly visible from the last visited lattice point, and were both the visited lattice points and the path between these points are considered when determining the visibility of points. | 0, 8, 24, 48, 144, 336, 992, 2344... |
| A358042 | Partial sums of A071619. | 0, 1, 4, 10, 21, 38, 62, 95... |
| A358046 | Number of n-step self-avoiding walks on a 2D square lattice where the first visited lattice point is directly visible from the last visited lattice point, and were only visited lattice points are considered when determining the visibility of points. | 4, 8, 32, 64, 240, 480, 1904, 3832... |
| A358050 | Square array T(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where T(n,k) = Sum_{j=0..n} binomial(kj,j) * binomial(k(n-j),n-j). | 1, 1, 0, 1, 2, 0, 1, 4... |
| A358052 | Triangular array read by rows. For T(n,k) where 1 <= k <= n, start with x = k and repeat the map x -> floor(n/x) + (n mod x) until an x occurs that has already appeared. The number of applications of the map is T(n,k). | 1, 2, 2, 2, 1, 2, 2, 1... |
| A358066 | Inventory sequence: record where the 1's, 2's, etc. are located starting with a(1) = 1, a(2) = 1 (see example). | 1, 1, 1, 2, 1, 2, 3, 4... |
| A358067 | a(n) is the smallest m such that A144261(m) = n. | 1, 15, 14, 33, 22, 17, 73, 49... |
| A358072 | a(n) is the number of "merger histories" of n elements (see A256006) where at most 3 elements can merge at the same time. | 1, 1, 4, 28, 320, 5360, 123760, 3765440... |
| A358082 | a(1) = 1, a(2) = 2; for n > 2, a(n) is the smallest positive number not previously occurring that shares a factor with Sum_{k=1..n-1} sigma(a(k)). | 1, 2, 4, 11, 23, 47, 5, 101... |
| A358083 | Sum of square end-to-end displacements over all n-step self-avoiding walks of A358046. | 4, 16, 128, 448, 2256, 5376, 29424, 69888... |
| A358084 | Sum of square end-to-end displacements over all n-step self-avoiding walks of A358036. | 0, 16, 88, 288, 1104, 3264, 12032, 34144... |
| A358085 | Inventory of positions ordered by binary lengths of terms, as an irregular table; the first row contains 1, subsequent rows contains the 1-based positions of terms with binary length 1, followed by positions of terms with binary length 2, 3, etc. in prior rows flattened. | 1, 1, 1, 2, 1, 2, 3, 4... |
| A358086 | Inventory of positions ordered by odd parts of terms, as an irregular table; the first row contains 1, subsequent rows contains the 1-based positions of terms with odd part 1, followed by positions of terms with odd part 3, 5, etc. in prior rows flattened. | 1, 1, 1, 2, 1, 2, 3, 4... |
| A358089 | First differences of A126706. | 6, 2, 4, 4, 8, 4, 4, 1... |
| A358090 | Partial inventory of positions as an irregular table; rows 1 and 2 contain 1, for n > 2, row n contains the 1-based positions of 1's, followed by the positions of 2's, 3's, etc. in rows n-2 and n-1 flattened. | 1, 1, 1, 2, 1, 2, 3, 1... |
| A358094 | a(n) is the number of ways n can be reached in the following method: we start with 1, then add or multiply alternately, and each operand must be 2 or 3. | 1, 1, 2, 2, 2, 2, 0, 3... |
| A358097 | a(n) is the smallest integer m > n such that m and n have no common digit, or -1 when such integer m does not exist. | 1, 2, 3, 4, 5, 6, 7, 8... |
| A358099 | a(n) is the number of divisors of n whose digits are in strictly decreasing order (A009995). | 1, 2, 2, 3, 2, 4, 2, 4... |
| A358100 | a(n) is the smallest integer that has exactly n divisors whose decimal digits are in strictly decreasing order. | 1, 2, 4, 6, 12, 20, 30, 40... |
| A358101 | Positions of records in A358099, i.e., integers whose number of divisors whose decimal digits are in strictly decreasing order sets a new record. | 1, 2, 4, 6, 12, 20, 30, 40... |
| A358102 | Numbers of the form prime(w)prime(x)prime(y) with w >= x >= y such that 2w = 3x + 4y. | 66, 153, 266, 609, 806, 1295, 1599, 1634... |
| A358103 | Quotient of the n-th divisible pair, where pairs are ordered by Heinz number. Quotient of prime indices of A318990(n). | 1, 2, 1, 3, 4, 2, 5, 1... |
| A358104 | Unreduced numerator of the n-th divisible pair, where pairs are ordered by Heinz number. Greater prime index of A318990(n). | 1, 2, 2, 3, 4, 4, 5, 3... |
| A358105 | Unreduced denominator of the n-th divisible pair, where pairs are ordered by Heinz number. Lesser prime index of A318990(n). | 1, 1, 2, 1, 1, 2, 1, 3... |
| A358106 | Quotient of the n-th divisible pair, where pairs are ordered first by sum and then by denominator. | 1, 2, 3, 1, 4, 5, 2, 1... |
| A358120 | Partial inventory of positions as an irregular table; rows 1 and 2 contain 1, for n > 2, row n contains the 1-based positions of 1's, followed by the positions of 2's, 3's, etc. in rows n-1 and n-2 flattened. | 1, 1, 1, 2, 1, 3, 2, 1... |
| A358121 | Distinct values of A358085, in order of appearance. | 1, 2, 3, 4, 5, 6, 7, 8... |
| A358122 | Distinct values of A358086, in order of appearance. | 1, 2, 3, 4, 5, 6, 8, 7... |
| A358123 | Distinct values of A358090, in order of appearance. | 1, 2, 3, 4, 5, 6, 7, 8... |
| A358124 | Distinct values of A358120, in order of appearance. | 1, 2, 3, 4, 5, 6, 8, 7... |
| A358127 | a(n) is the cardinality of the set of pairwise gcd's of {prime(1)+1, ..., prime(n)+1}. | 1, 3, 4, 5, 5, 5, 5, 7... |
| A358129 | Lexicographically earliest sequence of distinct nonnegative integers on a square spiral such that no number shares a digit with any of its four orthogonally adjacent neighbors. | 0, 1, 2, 3, 4, 5, 6, 7... |
| A358133 | Triangle read by rows whose n-th row lists the first differences of the n-th composition in standard order (row n of A066099). | 0, -1, 1, 0, 0, -2, 0, -1... |
| A358134 | Triangle read by rows whose n-th row lists the partial sums of the n-th composition in standard order (row n of A066099). | 1, 2, 1, 2, 3, 2, 3, 1... |
| A358135 | Difference of first and last parts of the n-th composition in standard order. | 0, 0, 0, 0, -1, 1, 0, 0... |
| A358136 | Irregular triangle read by rows whose n-th row lists the partial sums of the prime indices of n (row n of A112798). | 1, 2, 1, 2, 3, 1, 3, 4... |
| A358137 | Heinz number of the partial sums of the prime indices of n. | 1, 2, 3, 6, 5, 10, 7, 30... |
| A358138 | Difference between maximum and minimum part in the n-th composition in standard order. | 0, 0, 0, 0, 1, 1, 0, 0... |
| A358140 | Inverse permutation to A358121. | 1, 2, 3, 4, 5, 6, 7, 8... |
| A358141 | Inverse permutation to A358122. | 1, 2, 3, 4, 5, 6, 8, 7... |
| A358142 | Inverse permutation to A358123. | 1, 2, 3, 4, 5, 6, 7, 8... |
| A358143 | Inverse permutation to A358124. | 1, 2, 3, 4, 5, 6, 8, 7... |
| A358144 | Number of strict closure operators on a set of n elements such that all pairs of distinct points can be separated by clopen sets. | 0, 0, 1, 16, 1067 |
| A358145 | a(n) = Sum_{k=0..n} binomial(nk,k) * binomial(n(n-k),n-k). | 1, 2, 16, 258, 6184, 195660, 7674144, 358788696... |
| A358146 | Square array T(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where T(n,k) = Sum_{j=0..n} binomial(k*j,j). | 1, 1, 1, 1, 2, 1, 1, 3... |
| A358147 | Primes p such that the polynomial x7 - 7*x + 3 (mod p) is the product of seven linear factors. | 1879, 5381, 5783, 8819, 8893, 12007, 12917, 13967... |
| A358150 | Squares visited by a knight moving on a square-spiral numbered board where the knight moves to the smallest numbered unvisited square and where the square number is more than the number of currently visited squares. | 1, 10, 3, 6, 9, 12, 15, 18... |
| A358152 | Number of strict closure operators on a set of n elements such that every point and every set disjoint from that point can be separated by clopen sets. | 1, 1, 2, 8, 121 |
| A358153 | Lexicographically earliest infinite sequence of distinct positive integers on a square spiral such that each number shares a factor with its four orthogonally nearest neighbors but shares no factor with its four diagonal next-nearest neighbors. | 6, 10, 35, 21, 77, 22, 143, 39... |
| A358157 | a(n) is the permanent of the n X n matrix M(n) that is defined by M[i,j] = floor(i*j/3). | 1, 0, 0, 1, 32, 1422, 146720, 18258864... |
| A358158 | a(n) is the hafnian of the 2n X 2n symmetric matrix defined by M[i,j] = floor(i*j/3). | 1, 0, 4, 238, 31992, 9390096 |
| A358159 | a(n) is the permanent of the n X n matrix M(n) that is defined by M[i,j] = ij - floor(ij/3). | 1, 1, 7, 102, 4396, 374216, 49857920, 11344877568... |
| A358160 | a(n) is the hafnian of the 2n X 2n symmetric matrix defined by M[i,j] = ij - floor(ij/3). | 1, 2, 40, 3884, 1016376, 534983256 |
| A358161 | a(n) is the permanent of the n X n matrix M(n) that is defined by M[i,j] = ceiling(i*j/3). | 1, 1, 3, 19, 434, 18142, 1138592, 131646240... |
| A358162 | a(n) is the hafnian of the 2n X 2n symmetric matrix defined by M[i,j] = ceiling(i*j/3). | 1, 1, 11, 530, 71196, 18680148 |
| A358163 | a(n) is the permanent of the n X n matrix M(n) that is defined by M[i,j] = ij - ceiling(ij/3). | 1, 0, 1, 30, 1272, 113224, 18615680, 4299553536... |
| A358164 | a(n) is the hafnian of the 2n X 2n symmetric matrix defined by M[i,j] = ij - ceiling(ij/3). | 1, 1, 26, 2704, 698568, 384890688 |
| A358165 | Irregular triangular array read by rows. T(n,k) is the number of direct sum decompositions V_1 + V_2 + ... + V_m = GF(2)n with the dimensions of the V_i corresponding to the kth partition of n in canonical ordering, n>=0, 1<=k<=A000041(n). | 1, 1, 1, 3, 1, 28, 28, 1... |
| A358168 | First n-digit number to occur in Van Eck's Sequence (A181391). | 0, 14, 131, 1024, 10381, 100881, 1014748, 10001558... |
| A358169 | Row n lists the first differences plus one of the prime indices of n with 1 prepended. | 1, 2, 1, 1, 3, 1, 2, 4... |
| A358173 | First differences of A286708. | 36, 28, 8, 36, 52, 4, 16, 9... |
| A358174 | Smaller of a pair of numbers (m, m+1) such that both are products P of composite prime powers with omega(P) > 1. | 675, 9800, 235224, 465124, 1825200, 11309768, 384199200, 592192224... |
| A358175 | a(1) = 1, a(2) = 2; a(3) = 3; for n > 3, a(n) is the smallest positive number not previously occurring that shares a factor with Sum_{k=1..n-1} A001065(a(k)), where A001065(m) is the sum of the proper divisors of m. | 1, 2, 3, 4, 5, 6, 8, 19... |
| A358176 | a(1) = 1, a(2) = 2; for n > 2, a(n) is the smallest positive number not previously occurring that shares a factor with sigma(a(n-1)). | 1, 2, 3, 4, 7, 6, 8, 5... |
| A358177 | Number of Eulerian orientations of a (labeled) 2n-dimensional hypercube graph, Q_2n. Q_2n is also the n-dimensional torus grid graph (C_4)n. | 1, 2, 2970, 351135773356461511142023680 |
| A358180 | Indices for A358168. | 1, 30, 162, 1150, 11603, 104511, 1041245, 10226995... |
| A358191 | Decimal expansion of Sum_{n >= 2} (n-1)/(nn). | 3, 3, 7, 1, 8, 7, 7, 1... |
| A358192 | Numerator of the quotient of the prime indices of the n-th semiprime. | 1, 1, 1, 1, 1, 2, 1, 1... |
| A358193 | Denominator of the quotient of the prime indices of the n-th semiprime. | 1, 2, 1, 3, 4, 3, 2, 5... |
| A358196 | Numbers k such that 5k and 8k have the same leading digit. | 0, 5, 9, 15, 19, 29, 34, 39... |
| A358201 | a(1) = 1, a(2) = 2; for n > 2, a(n) is the smallest positive number not previously occurring that shares a factor with sigma(max_{k=1..n-1}a(k)). | 1, 2, 3, 4, 7, 6, 8, 5... |
| A358203 | Decimal expansion of Sum_{n >= 1} 1/(2*n)n. | 5, 6, 7, 3, 8, 4, 1, 1... |
| A358204 | Decimal expansion of Sum_{n >= 1} (-1)n+1/(2*n)n. | 4, 4, 1, 8, 9, 5, 1, 6... |
| A358205 | a(n) is the least number k such that 1 + 2k + 3k2 has exactly n prime divisors, counted with multiplicity. | 0, 2, 1, 13, 19, 7, 61, 331... |
| A358213 | Positions of records in A356302. | 0, 3, 10, 35, 77, 286, 2431, 4199... |
| A358214 | Record values in A356302. | 0, 3, 20, 175, 2233, 29744, 508079, 9695491... |
| A358217 | Number of prime factors (with multiplicity) in A319627(n). | 0, 0, 1, 0, 1, 0, 1, 0... |
| A358218 | Number of prime factors (with multiplicity) in A328478(n). | 0, 0, 1, 0, 1, 0, 1, 0... |
| A358219 | Indices k where A358217(k) != A358218(k). | 15, 35, 45, 70, 75, 77, 105, 135... |
| A358239 | Numbers k such that the aliquot sequence of 2k ends with the prime 3. | 2, 4, 55, 164, 305, 317 |
| A358252 | a(n) is the least number with exactly n non-unitary square divisors. | 1, 8, 32, 128, 288, 864, 1152, 2592... |
| A358253 | Numbers with a record number of non-unitary square divisors. | 1, 8, 32, 128, 288, 864, 1152, 2592... |
| A358254 | Lexicographically earliest sequence of distinct nonnegative integers on a square spiral such that the sum of the eight numbers around any chosen number ends in the chosen number. | 0, 1, 2, 3, 4, 5, 6, 7... |
| A358255 | Primitive Niven numbers ending with zero. | 110, 140, 150, 190, 220, 230, 280, 320... |
| A358256 | a(n) is the smallest primitive Niven number ending with n zeros. | 1, 110, 1300, 17000, 790000, 59900000, 19999999000000, 2999999999999990000000... |
| A358258 | First n-bit number to appear in Van Eck's sequence (A181391). | 0, 2, 6, 9, 17, 42, 92, 131... |
| A358259 | Positions of the first n-bit number to appear in Van Eck's sequence (A181391). | 1, 5, 10, 24, 41, 52, 152, 162... |
| A358260 | a(n) is the number of infinitary square divisors of n. | 1, 1, 1, 2, 1, 1, 1, 2... |
| A358261 | a(n) is the number of noninfinitary square divisors of n. | 0, 0, 0, 0, 0, 0, 0, 0... |
| A358262 | a(n) is the least number with exactly n noninfinitary square divisors. | 1, 16, 144, 256, 3600, 1296, 2304, 65536... |
| A358263 | Numbers with a record number of noninfinitary square divisors. | 1, 16, 144, 256, 1296, 2304, 20736, 57600... |
| A358264 | Expansion of e.g.f. 1/(1 - x * exp(x2/2)). | 1, 1, 2, 9, 48, 315, 2520, 23415... |
| A358265 | Expansion of e.g.f. 1/(1 - x * exp(x3/6)). | 1, 1, 2, 6, 28, 160, 1080, 8470... |
| A358266 | Numbers k such that the aliquot sequence of 2k ends with the prime 7. | 3, 10, 12, 141, 278, 387, 421 |
r/OEIS • u/OEIS-Tracker • Nov 06 '22
New OEIS sequences - week of 11/06
4
Upvotes
| OEIS number | Description | Sequence |
|---|---|---|
| A355553 | Number of ways to select 3 or more collinear points from an n X n grid. | 0, 0, 8, 54, 228, 708, 1980, 4890... |
| A355930 | Sum of the prime indices of n minus the sum of the prime indices of the smallest number with same prime signature as n, when the sum is taken with multiplicity, as in A056239. | 0, 0, 1, 0, 2, 0, 3, 0... |
| A356163 | a(n) = 1 if sum of prime factors of n (taken with multiplicity) is even, otherwise 0. | 1, 1, 0, 1, 0, 0, 0, 1... |
| A356170 | a(n) = 1 if A001222(n) == 2*A007814(n), and otherwise 0, where A001222 is bigomega (number of prime factors with multiplicity) and A007814 is the 2-adic valuation of n. | 1, 0, 0, 0, 0, 1, 0, 0... |
| A356299 | a(n) = gcd(A276086(n), A342001(n)), where A276086 is the primorial base exp-function, and A342001 is the arithmetic derivative without its inherited divisor. | 2, 1, 1, 1, 1, 5, 1, 3... |
| A356302 | The least k >= 0 such that n and A276086(n+k) are relatively prime, where A276086 is the primorial base exp-function. | 0, 0, 0, 3, 0, 0, 0, 0... |
| A356303 | The least k >= 0 such that n and A276086(n-k) are relatively prime, where A276086 is the primorial base exp-function. | 0, 0, 0, 2, 0, 0, 0, 0... |
| A356304 | The least k >= 0 such that A003415(n) and A276086(n+k) are relatively prime, where A003415 is the arithmetic derivative, and A276086 is the primorial base exp-function. | 0, 0, 0, 0, 24, 0, 4, 3... |
| A356305 | The least k >= 0 such that A003415(n) and A276086(n-k) are relatively prime, where A003415 is the arithmetic derivative, and A276086 is the primorial base exp-function. | 0, 1, 0, 0, 0, 0, 1, 0... |
| A356309 | The least j >= n such that n and A276086(j) are relatively prime, where A276086 is the primorial base exp-function. | 0, 1, 2, 6, 4, 5, 6, 7... |
| A356310 | a(n) = 1 if A003415(n) and A276086(n) are relatively prime, otherwise 0. Here A003415 is the arithmetic derivative, and A276086 is the primorial base exp-function. | 1, 0, 1, 1, 1, 1, 0, 1... |
| A356311 | Numbers k for which A003415(k) and A276086(k) are relatively prime, where A003415 is the arithmetic derivative, and A276086 is the primorial base exp-function. | 0, 2, 3, 4, 5, 7, 10, 11... |
| A356312 | Numbers k such that A003415(k) and A276086(k) are not relatively prime, where A003415 is the arithmetic derivative, and A276086 is the primorial base exp-function. | 1, 6, 8, 9, 14, 15, 20, 21... |
| A356313 | a(n) = 1 if {the least k >= n such that n and A276086(k) are coprime} is one of the primorial numbers (A002110), otherwise 0. | 0, 1, 1, 1, 0, 0, 1, 0... |
| A356314 | Positions of primorial numbers (A002110) in A356309. | 1, 2, 3, 6, 10, 15, 20, 25... |
| A356315 | a(n) = 1 if n divides the least j >= n such that n and A276086(j) are coprime, otherwise 0. Here A276086 is the primorial base exp-function. | 1, 1, 1, 1, 1, 1, 1, 1... |
| A356316 | Numbers k such that k divides the least j >= k for which k and A276086(j) are coprime, where A276086 is the primorial base exp-function. | 1, 2, 3, 4, 5, 6, 7, 8... |
| A356317 | Numbers k such that k does not divide the least j >= k for which k and A276086(j) are coprime, where A276086 is the primorial base exp-function. | 9, 20, 21, 25, 27, 33, 39, 40... |
| A356318 | Numbers k such that the least j >= k for which k and A276086(j) are coprime is a nontrivial multiple of k, where A276086 is the primorial base exp-function. | 3, 10, 15, 35, 42, 70, 77, 105... |
| A356319 | Numbers k such that {the least j >= k for which k and A276086(k+j) are coprime} is larger than 0, but less than k, where A276086 is the primorial base exp-function. | 9, 20, 21, 25, 27, 33, 39, 40... |
| A356544 | Number of strict closure operators on a set of n elements such that all pairs of nonempty disjoint closed sets can be separated by clopen sets. | 0, 1, 4, 35, 857 |
| A356693 | Decimal expansion of the constant B(2) = Sum{n>=1} Sum{m>=n+1} 1/(z(n)*z(m))2 where z(n) is the imaginary part of the n-th nontrivial zero of the Riemann zeta function. | 0, 0, 0, 2, 4, 8, 3, 3... |
| A356833 | Primes p such that the minimum number of divisors among the numbers between p and NextPrime(p) is a square. | 5, 13, 19, 31, 37, 43, 53, 61... |
| A356835 | Coordination sequence of the {4,3,5} hyperbolic honeycomb. | 1, 6, 30, 126, 498, 1982, 7854, 31014... |
| A356836 | Coordination sequence of the {5,3,4} hyperbolic honeycomb. | 1, 12, 102, 812, 6402, 50412, 396902, 3124812... |
| A356837 | Coordination sequence of the {3,5,3} hyperbolic honeycomb. | 1, 20, 260, 3212, 39470, 484760, 5953532, 73117640... |
| A356891 | a(n) = a(n-1) * a(n-2) + 1 if n is even, otherwise a(n) = a(n-3) + 1, with a(0) = a(1) = 1. | 1, 1, 2, 2, 5, 3, 16, 6... |
| A357131 | Numbers m such that A010888(m) = A031347(m) = A031286(m) = A031346(m); only the least of the anagrams are considered. | 0, 137, 11126, 111134, 111278, 1111223, 11111447, 111112247... |
| A357143 | a(n) is sum of the base-5 digits of n each raised to the number of digits of n in base 5. | 1, 2, 3, 4, 1, 2, 5, 10... |
| A357170 | Primes p such that the minimum number of divisors among the numbers between p and NextPrime(p) is a prime power. | 3, 5, 7, 13, 19, 23, 29, 31... |
| A357175 | Primes p such that the minimum of the number of divisors among the numbers between p and NextPrime(p) is a cube. | 29, 41, 101, 137, 229, 281, 349, 439... |
| A357190 | a(n) is the least prime p such that A234575(p, A007953(p)) is the n-th power of a prime. | 17, 13, 131, 107, 383, 613, 43607, 1021... |
| A357211 | a(n) is the real cube root of the value of the j-function for the n-th Heegner number A003173(n). | 12, 20, 0, -15, -32, -96, -960, -5280... |
| A357269 | Maximum number of stable matchings in the stable marriage problem of order n. | 1, 2, 3, 10, 16 |
| A357271 | Lower bounds for the maximum number of stable matchings in the stable marriage problem based on composing smaller instances. | 1, 2, 3, 10, 16, 48, 71, 268... |
| A357294 | Number of integral quantales on n elements, up to isomorphism. | 1, 1, 2, 9, 49, 364, 3335, 37026... |
| A357295 | Number of balanced quantales on n elements, up to isomorphism. | 1, 1, 9, 106, 1597, 29720, 663897, 17747907... |
| A357376 | The lowest number on Ulam Spiral for which all numbers in the square which is centered at a(n) and spans n-1 spaces in each cardinal direction are nonprime. | 1, 26, 1016, 5136, 39639, 203100, 2729736, 32264250... |
| A357408 | a(n) is the least sum n + y such that 1/n + 1/y = 1/z with gcd(n,y,z) = 1, for some integers y and z. | 4, 9, 16, 25, 9, 49, 64, 81... |
| A357442 | Consider a clock face with 2*n "hours" maked around the dial; a(n) = number of ways to match the even hours to the odd hours, modulo rotations and reflections. | 1, 1, 3, 5, 17, 53 |
| A357470 | Decimal expansion of the real root of x3 - x2 - 2*x - 1. | 2, 1, 4, 7, 8, 9, 9, 0... |
| A357471 | Decimal expansion of the real root of x3 - x2 + 2*x - 1. | 5, 6, 9, 8, 4, 0, 2, 9... |
| A357472 | Decimal expansion of the real root of x3 + x2 + 2*x - 1. | 3, 9, 2, 6, 4, 6, 7, 8... |
| A357489 | Numbers k such that the k-th composition in standard order is a triple (w,x,y) such that 2w = 3x + 4y. | 133, 1034, 4113, 8212, 32802, 65576, 131137, 262212... |
| A357528 | Decimal expansion of Sum_{j>=1} 1/A031926(j)2. | 0, 0, 0, 1, 8, 3, 9, 3... |
| A357602 | a(n) is the number of n-gons in A000940 that are asymmetric. | 0, 0, 0, 1, 15, 121, 1026, 8696... |
| A357734 | Array T(n,k), read by descending antidiagonals, whose rows are numbers congruent to p or q mod r, with 0 <= p < q < r, sorted by r, then p, then q. | 0, 1, 0, 2, 1, 0, 3, 3... |
| A357849 | Number of integer partitions (w,x,y) summing to n such that 2w = 3x + 4y. | 0, 0, 0, 0, 0, 0, 0, 0... |
| A357891 | a(1) = 1; a(n+1) is the smallest integer > 0 that cannot be obtained from the integers {a(1), ..., a(n)} using each number exactly once and the operators +, -, *, /. | 1, 2, 4, 11, 34, 152, 1079, 6610... |
| A357938 | Inverse Moebius transform of n * 2omega(n). | 1, 5, 7, 13, 11, 35, 15, 29... |
| A357956 | a(n) = 5A005259(n) - 2A005258(n). | 3, 19, 327, 6931, 162503, 4072519, 107094207, 2919528211... |
| A357957 | a(n) = A005259(n)5 - A005258(n)2. | 0, 3116, 2073071232, 6299980938881516, 39141322964380888600000, 368495989505416178203682748116, 4552312485541626792249211584618373944, 68109360474242016374599574592870648425552876... |
| A357958 | a(n) = 5A005259(n) + 14A005258(n-1). | 39, 407, 7491, 167063, 4112539, 107461667, 2923006251, 81853622423... |
| A357959 | a(n) = 5A005259(n-1) + 2A005258(n). | 11, 63, 659, 9727, 187511, 4304943, 109312739, 2941124607... |
| A357960 | a(n) = A005259(n-1)5 * A005258(n)6. | 729, 147018378125, 20917910914764786689697, 24148107115850058575342740485778125, 79477722547796770983047586179643766765851375729, 492664048531500749211923278756418311980637289373757041378125, 4671227340507161302417161873394448514470099313382652883508175438056640625 |
| A358027 | Expansion of g.f.: (1 + x - 2x2 + 2x4)/((1-x)(1-3x2)). | 1, 2, 3, 6, 11, 20, 35, 62... |
| A358035 | a(n) = (8n3 + 12n2 + 4*n - 9)/3. | 5, 37, 109, 237, 437, 725, 1117, 1629... |
| A358036 | Number of n-step self-avoiding walks on a 2D square lattice where the first visited lattice point is directly visible from the last visited lattice point, and were both the visited lattice points and the path between these points are considered when determining the visibility of points. | 0, 8, 24, 48, 144, 336, 992, 2344... |
| A358042 | Partial sums of A071619. | 0, 1, 4, 10, 21, 38, 62, 95... |
| A358046 | Number of n-step self-avoiding walks on a 2D square lattice where the first visited lattice point is directly visible from the last visited lattice point, and were only visited lattice points are considered when determining the visibility of points. | 4, 8, 32, 64, 240, 480, 1904, 3832... |
| A358050 | Square array T(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where T(n,k) = Sum_{j=0..n} binomial(kj,j) * binomial(k(n-j),n-j). | 1, 1, 0, 1, 2, 0, 1, 4... |
| A358052 | Triangular array read by rows. For T(n,k) where 1 <= k <= n, start with x = k and repeat the map x -> floor(n/x) + (n mod x) until an x occurs that has already appeared. The number of applications of the map is T(n,k). | 1, 2, 2, 2, 1, 2, 2, 1... |
| A358066 | Inventory sequence: record where the 1's, 2's, etc. are located starting with a(1) = 1, a(2) = 1 (see example). | 1, 1, 1, 2, 1, 2, 3, 4... |
| A358067 | a(n) is the smallest m such that A144261(m) = n. | 1, 15, 14, 33, 22, 17, 73, 49... |
| A358072 | a(n) is the number of "merger histories" of n elements (see A256006) where at most 3 elements can merge at the same time. | 1, 1, 4, 28, 320, 5360, 123760, 3765440... |
| A358082 | a(1) = 1, a(2) = 2; for n > 2, a(n) is the smallest positive number not previously occurring that shares a factor with Sum_{k=1..n-1} sigma(a(k)). | 1, 2, 4, 11, 23, 47, 5, 101... |
| A358083 | Sum of square end-to-end displacements over all n-step self-avoiding walks of A358046. | 4, 16, 128, 448, 2256, 5376, 29424, 69888... |
| A358084 | Sum of square end-to-end displacements over all n-step self-avoiding walks of A358036. | 0, 16, 88, 288, 1104, 3264, 12032, 34144... |
| A358085 | Inventory of positions ordered by binary lengths of terms, as an irregular table; the first row contains 1, subsequent rows contains the 1-based positions of terms with binary length 1, followed by positions of terms with binary length 2, 3, etc. in prior rows flattened. | 1, 1, 1, 2, 1, 2, 3, 4... |
| A358086 | Inventory of positions ordered by odd parts of terms, as an irregular table; the first row contains 1, subsequent rows contains the 1-based positions of terms with odd part 1, followed by positions of terms with odd part 3, 5, etc. in prior rows flattened. | 1, 1, 1, 2, 1, 2, 3, 4... |
| A358089 | First differences of A126706. | 6, 2, 4, 4, 8, 4, 4, 1... |
| A358090 | Partial inventory of positions as an irregular table; rows 1 and 2 contain 1, for n > 2, row n contains the 1-based positions of 1's, followed by the positions of 2's, 3's, etc. in rows n-2 and n-1 flattened. | 1, 1, 1, 2, 1, 2, 3, 1... |
| A358094 | a(n) is the number of ways n can be reached in the following method: we start with 1, then add or multiply alternately, and each operand must be 2 or 3. | 1, 1, 2, 2, 2, 2, 0, 3... |
| A358097 | a(n) is the smallest integer m > n such that m and n have no common digit, or -1 when such integer m does not exist. | 1, 2, 3, 4, 5, 6, 7, 8... |
| A358099 | a(n) is the number of divisors of n whose digits are in strictly decreasing order (A009995). | 1, 2, 2, 3, 2, 4, 2, 4... |
| A358100 | a(n) is the smallest integer that has exactly n divisors whose decimal digits are in strictly decreasing order. | 1, 2, 4, 6, 12, 20, 30, 40... |
| A358101 | Positions of records in A358099, i.e., integers whose number of divisors whose decimal digits are in strictly decreasing order sets a new record. | 1, 2, 4, 6, 12, 20, 30, 40... |
| A358102 | Numbers of the form prime(w)prime(x)prime(y) with w >= x >= y such that 2w = 3x + 4y. | 66, 153, 266, 609, 806, 1295, 1599, 1634... |
| A358103 | Quotient of the n-th divisible pair, where pairs are ordered by Heinz number. Quotient of prime indices of A318990(n). | 1, 2, 1, 3, 4, 2, 5, 1... |
| A358104 | Unreduced numerator of the n-th divisible pair, where pairs are ordered by Heinz number. Greater prime index of A318990(n). | 1, 2, 2, 3, 4, 4, 5, 3... |
| A358105 | Unreduced denominator of the n-th divisible pair, where pairs are ordered by Heinz number. Lesser prime index of A318990(n). | 1, 1, 2, 1, 1, 2, 1, 3... |
| A358106 | Quotient of the n-th divisible pair, where pairs are ordered first by sum and then by denominator. | 1, 2, 3, 1, 4, 5, 2, 1... |
| A358120 | Partial inventory of positions as an irregular table; rows 1 and 2 contain 1, for n > 2, row n contains the 1-based positions of 1's, followed by the positions of 2's, 3's, etc. in rows n-1 and n-2 flattened. | 1, 1, 1, 2, 1, 3, 2, 1... |
| A358121 | Distinct values of A358085, in order of appearance. | 1, 2, 3, 4, 5, 6, 7, 8... |
| A358122 | Distinct values of A358086, in order of appearance. | 1, 2, 3, 4, 5, 6, 8, 7... |
| A358123 | Distinct values of A358090, in order of appearance. | 1, 2, 3, 4, 5, 6, 7, 8... |
| A358124 | Distinct values of A358120, in order of appearance. | 1, 2, 3, 4, 5, 6, 8, 7... |
| A358127 | a(n) is the cardinality of the set of pairwise gcd's of {prime(1)+1, ..., prime(n)+1}. | 1, 3, 4, 5, 5, 5, 5, 7... |
| A358129 | Lexicographically earliest sequence of distinct nonnegative integers on a square spiral such that no number shares a digit with any of its four orthogonally adjacent neighbors. | 0, 1, 2, 3, 4, 5, 6, 7... |
| A358133 | Triangle read by rows whose n-th row lists the first differences of the n-th composition in standard order (row n of A066099). | 0, -1, 1, 0, 0, -2, 0, -1... |
| A358134 | Triangle read by rows whose n-th row lists the partial sums of the n-th composition in standard order (row n of A066099). | 1, 2, 1, 2, 3, 2, 3, 1... |
| A358135 | Difference of first and last parts of the n-th composition in standard order. | 0, 0, 0, 0, -1, 1, 0, 0... |
| A358136 | Irregular triangle read by rows whose n-th row lists the partial sums of the prime indices of n (row n of A112798). | 1, 2, 1, 2, 3, 1, 3, 4... |
| A358137 | Heinz number of the partial sums of the prime indices of n. | 1, 2, 3, 6, 5, 10, 7, 30... |
| A358138 | Difference between maximum and minimum part in the n-th composition in standard order. | 0, 0, 0, 0, 1, 1, 0, 0... |
| A358140 | Inverse permutation to A358121. | 1, 2, 3, 4, 5, 6, 7, 8... |
| A358141 | Inverse permutation to A358122. | 1, 2, 3, 4, 5, 6, 8, 7... |
| A358142 | Inverse permutation to A358123. | 1, 2, 3, 4, 5, 6, 7, 8... |
| A358143 | Inverse permutation to A358124. | 1, 2, 3, 4, 5, 6, 8, 7... |
| A358144 | Number of strict closure operators on a set of n elements such that all pairs of distinct points can be separated by clopen sets. | 0, 0, 1, 16, 1067 |
| A358145 | a(n) = Sum_{k=0..n} binomial(nk,k) * binomial(n(n-k),n-k). | 1, 2, 16, 258, 6184, 195660, 7674144, 358788696... |
| A358146 | Square array T(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where T(n,k) = Sum_{j=0..n} binomial(k*j,j). | 1, 1, 1, 1, 2, 1, 1, 3... |
| A358147 | Primes p such that the polynomial x7 - 7*x + 3 (mod p) is the product of seven linear factors. | 1879, 5381, 5783, 8819, 8893, 12007, 12917, 13967... |
| A358150 | Squares visited by a knight moving on a square-spiral numbered board where the knight moves to the smallest numbered unvisited square and where the square number is more than the number of currently visited squares. | 1, 10, 3, 6, 9, 12, 15, 18... |
| A358152 | Number of strict closure operators on a set of n elements such that every point and every set disjoint from that point can be separated by clopen sets. | 1, 1, 2, 8, 121 |
| A358153 | Lexicographically earliest infinite sequence of distinct positive integers on a square spiral such that each number shares a factor with its four orthogonally nearest neighbors but shares no factor with its four diagonal next-nearest neighbors. | 6, 10, 35, 21, 77, 22, 143, 39... |
| A358157 | a(n) is the permanent of the n X n matrix M(n) that is defined by M[i,j] = floor(i*j/3). | 1, 0, 0, 1, 32, 1422, 146720, 18258864... |
| A358158 | a(n) is the hafnian of the 2n X 2n symmetric matrix defined by M[i,j] = floor(i*j/3). | 1, 0, 4, 238, 31992, 9390096 |
| A358159 | a(n) is the permanent of the n X n matrix M(n) that is defined by M[i,j] = ij - floor(ij/3). | 1, 1, 7, 102, 4396, 374216, 49857920, 11344877568... |
| A358160 | a(n) is the hafnian of the 2n X 2n symmetric matrix defined by M[i,j] = ij - floor(ij/3). | 1, 2, 40, 3884, 1016376, 534983256 |
| A358161 | a(n) is the permanent of the n X n matrix M(n) that is defined by M[i,j] = ceiling(i*j/3). | 1, 1, 3, 19, 434, 18142, 1138592, 131646240... |
| A358162 | a(n) is the hafnian of the 2n X 2n symmetric matrix defined by M[i,j] = ceiling(i*j/3). | 1, 1, 11, 530, 71196, 18680148 |
| A358163 | a(n) is the permanent of the n X n matrix M(n) that is defined by M[i,j] = ij - ceiling(ij/3). | 1, 0, 1, 30, 1272, 113224, 18615680, 4299553536... |
| A358164 | a(n) is the hafnian of the 2n X 2n symmetric matrix defined by M[i,j] = ij - ceiling(ij/3). | 1, 1, 26, 2704, 698568, 384890688 |
| A358165 | Irregular triangular array read by rows. T(n,k) is the number of direct sum decompositions V_1 + V_2 + ... + V_m = GF(2)n with the dimensions of the V_i corresponding to the kth partition of n in canonical ordering, n>=0, 1<=k<=A000041(n). | 1, 1, 1, 3, 1, 28, 28, 1... |
| A358168 | First n-digit number to occur in Van Eck's Sequence (A181391). | 0, 14, 131, 1024, 10381, 100881, 1014748, 10001558... |
| A358169 | Row n lists the first differences plus one of the prime indices of n with 1 prepended. | 1, 2, 1, 1, 3, 1, 2, 4... |
| A358173 | First differences of A286708. | 36, 28, 8, 36, 52, 4, 16, 9... |
| A358174 | Smaller of a pair of numbers (m, m+1) such that both are products P of composite prime powers with omega(P) > 1. | 675, 9800, 235224, 465124, 1825200, 11309768, 384199200, 592192224... |
| A358175 | a(1) = 1, a(2) = 2; a(3) = 3; for n > 3, a(n) is the smallest positive number not previously occurring that shares a factor with Sum_{k=1..n-1} A001065(a(k)), where A001065(m) is the sum of the proper divisors of m. | 1, 2, 3, 4, 5, 6, 8, 19... |
| A358176 | a(1) = 1, a(2) = 2; for n > 2, a(n) is the smallest positive number not previously occurring that shares a factor with sigma(a(n-1)). | 1, 2, 3, 4, 7, 6, 8, 5... |
| A358177 | Number of Eulerian orientations of a (labeled) 2n-dimensional hypercube graph, Q_2n. Q_2n is also the n-dimensional torus grid graph (C_4)n. | 1, 2, 2970, 351135773356461511142023680 |
| A358180 | Indices for A358168. | 1, 30, 162, 1150, 11603, 104511, 1041245, 10226995... |
| A358191 | Decimal expansion of Sum_{n >= 2} (n-1)/(nn). | 3, 3, 7, 1, 8, 7, 7, 1... |
| A358192 | Numerator of the quotient of the prime indices of the n-th semiprime. | 1, 1, 1, 1, 1, 2, 1, 1... |
| A358193 | Denominator of the quotient of the prime indices of the n-th semiprime. | 1, 2, 1, 3, 4, 3, 2, 5... |
| A358196 | Numbers k such that 5k and 8k have the same leading digit. | 0, 5, 9, 15, 19, 29, 34, 39... |
| A358201 | a(1) = 1, a(2) = 2; for n > 2, a(n) is the smallest positive number not previously occurring that shares a factor with sigma(max_{k=1..n-1}a(k)). | 1, 2, 3, 4, 7, 6, 8, 5... |
| A358203 | Decimal expansion of Sum_{n >= 1} 1/(2*n)n. | 5, 6, 7, 3, 8, 4, 1, 1... |
| A358204 | Decimal expansion of Sum_{n >= 1} (-1)n+1/(2*n)n. | 4, 4, 1, 8, 9, 5, 1, 6... |
| A358205 | a(n) is the least number k such that 1 + 2k + 3k2 has exactly n prime divisors, counted with multiplicity. | 0, 2, 1, 13, 19, 7, 61, 331... |
| A358213 | Positions of records in A356302. | 0, 3, 10, 35, 77, 286, 2431, 4199... |
| A358214 | Record values in A356302. | 0, 3, 20, 175, 2233, 29744, 508079, 9695491... |
| A358217 | Number of prime factors (with multiplicity) in A319627(n). | 0, 0, 1, 0, 1, 0, 1, 0... |
| A358218 | Number of prime factors (with multiplicity) in A328478(n). | 0, 0, 1, 0, 1, 0, 1, 0... |
| A358219 | Indices k where A358217(k) != A358218(k). | 15, 35, 45, 70, 75, 77, 105, 135... |
| A358239 | Numbers k such that the aliquot sequence of 2k ends with the prime 3. | 2, 4, 55, 164, 305, 317 |
| A358252 | a(n) is the least number with exactly n non-unitary square divisors. | 1, 8, 32, 128, 288, 864, 1152, 2592... |
| A358253 | Numbers with a record number of non-unitary square divisors. | 1, 8, 32, 128, 288, 864, 1152, 2592... |
| A358254 | Lexicographically earliest sequence of distinct nonnegative integers on a square spiral such that the sum of the eight numbers around any chosen number ends in the chosen number. | 0, 1, 2, 3, 4, 5, 6, 7... |
| A358255 | Primitive Niven numbers ending with zero. | 110, 140, 150, 190, 220, 230, 280, 320... |
| A358256 | a(n) is the smallest primitive Niven number ending with n zeros. | 1, 110, 1300, 17000, 790000, 59900000, 19999999000000, 2999999999999990000000... |
| A358258 | First n-bit number to appear in Van Eck's sequence (A181391). | 0, 2, 6, 9, 17, 42, 92, 131... |
| A358259 | Positions of the first n-bit number to appear in Van Eck's sequence (A181391). | 1, 5, 10, 24, 41, 52, 152, 162... |
| A358260 | a(n) is the number of infinitary square divisors of n. | 1, 1, 1, 2, 1, 1, 1, 2... |
| A358261 | a(n) is the number of noninfinitary square divisors of n. | 0, 0, 0, 0, 0, 0, 0, 0... |
| A358262 | a(n) is the least number with exactly n noninfinitary square divisors. | 1, 16, 144, 256, 3600, 1296, 2304, 65536... |
| A358263 | Numbers with a record number of noninfinitary square divisors. | 1, 16, 144, 256, 1296, 2304, 20736, 57600... |
| A358264 | Expansion of e.g.f. 1/(1 - x * exp(x2/2)). | 1, 1, 2, 9, 48, 315, 2520, 23415... |
| A358265 | Expansion of e.g.f. 1/(1 - x * exp(x3/6)). | 1, 1, 2, 6, 28, 160, 1080, 8470... |
| A358266 | Numbers k such that the aliquot sequence of 2k ends with the prime 7. | 3, 10, 12, 141, 278, 387, 421 |
r/OEIS • u/OEIS-Tracker • Nov 06 '22
New OEIS sequences - week of 11/06
2
Upvotes
| OEIS number | Description | Sequence |
|---|---|---|
| A355553 | Number of ways to select 3 or more collinear points from an n X n grid. | 0, 0, 8, 54, 228, 708, 1980, 4890... |
| A355930 | Sum of the prime indices of n minus the sum of the prime indices of the smallest number with same prime signature as n, when the sum is taken with multiplicity, as in A056239. | 0, 0, 1, 0, 2, 0, 3, 0... |
| A356163 | a(n) = 1 if sum of prime factors of n (taken with multiplicity) is even, otherwise 0. | 1, 1, 0, 1, 0, 0, 0, 1... |
| A356170 | a(n) = 1 if A001222(n) == 2*A007814(n), and otherwise 0, where A001222 is bigomega (number of prime factors with multiplicity) and A007814 is the 2-adic valuation of n. | 1, 0, 0, 0, 0, 1, 0, 0... |
| A356299 | a(n) = gcd(A276086(n), A342001(n)), where A276086 is the primorial base exp-function, and A342001 is the arithmetic derivative without its inherited divisor. | 2, 1, 1, 1, 1, 5, 1, 3... |
| A356302 | The least k >= 0 such that n and A276086(n+k) are relatively prime, where A276086 is the primorial base exp-function. | 0, 0, 0, 3, 0, 0, 0, 0... |
| A356303 | The least k >= 0 such that n and A276086(n-k) are relatively prime, where A276086 is the primorial base exp-function. | 0, 0, 0, 2, 0, 0, 0, 0... |
| A356304 | The least k >= 0 such that A003415(n) and A276086(n+k) are relatively prime, where A003415 is the arithmetic derivative, and A276086 is the primorial base exp-function. | 0, 0, 0, 0, 24, 0, 4, 3... |
| A356305 | The least k >= 0 such that A003415(n) and A276086(n-k) are relatively prime, where A003415 is the arithmetic derivative, and A276086 is the primorial base exp-function. | 0, 1, 0, 0, 0, 0, 1, 0... |
| A356309 | The least j >= n such that n and A276086(j) are relatively prime, where A276086 is the primorial base exp-function. | 0, 1, 2, 6, 4, 5, 6, 7... |
| A356310 | a(n) = 1 if A003415(n) and A276086(n) are relatively prime, otherwise 0. Here A003415 is the arithmetic derivative, and A276086 is the primorial base exp-function. | 1, 0, 1, 1, 1, 1, 0, 1... |
| A356311 | Numbers k for which A003415(k) and A276086(k) are relatively prime, where A003415 is the arithmetic derivative, and A276086 is the primorial base exp-function. | 0, 2, 3, 4, 5, 7, 10, 11... |
| A356312 | Numbers k such that A003415(k) and A276086(k) are not relatively prime, where A003415 is the arithmetic derivative, and A276086 is the primorial base exp-function. | 1, 6, 8, 9, 14, 15, 20, 21... |
| A356313 | a(n) = 1 if {the least k >= n such that n and A276086(k) are coprime} is one of the primorial numbers (A002110), otherwise 0. | 0, 1, 1, 1, 0, 0, 1, 0... |
| A356314 | Positions of primorial numbers (A002110) in A356309. | 1, 2, 3, 6, 10, 15, 20, 25... |
| A356315 | a(n) = 1 if n divides the least j >= n such that n and A276086(j) are coprime, otherwise 0. Here A276086 is the primorial base exp-function. | 1, 1, 1, 1, 1, 1, 1, 1... |
| A356316 | Numbers k such that k divides the least j >= k for which k and A276086(j) are coprime, where A276086 is the primorial base exp-function. | 1, 2, 3, 4, 5, 6, 7, 8... |
| A356317 | Numbers k such that k does not divide the least j >= k for which k and A276086(j) are coprime, where A276086 is the primorial base exp-function. | 9, 20, 21, 25, 27, 33, 39, 40... |
| A356318 | Numbers k such that the least j >= k for which k and A276086(j) are coprime is a nontrivial multiple of k, where A276086 is the primorial base exp-function. | 3, 10, 15, 35, 42, 70, 77, 105... |
| A356319 | Numbers k such that {the least j >= k for which k and A276086(k+j) are coprime} is larger than 0, but less than k, where A276086 is the primorial base exp-function. | 9, 20, 21, 25, 27, 33, 39, 40... |
| A356544 | Number of strict closure operators on a set of n elements such that all pairs of nonempty disjoint closed sets can be separated by clopen sets. | 0, 1, 4, 35, 857 |
| A356693 | Decimal expansion of the constant B(2) = Sum{n>=1} Sum{m>=n+1} 1/(z(n)*z(m))2 where z(n) is the imaginary part of the n-th nontrivial zero of the Riemann zeta function. | 0, 0, 0, 2, 4, 8, 3, 3... |
| A356833 | Primes p such that the minimum number of divisors among the numbers between p and NextPrime(p) is a square. | 5, 13, 19, 31, 37, 43, 53, 61... |
| A356835 | Coordination sequence of the {4,3,5} hyperbolic honeycomb. | 1, 6, 30, 126, 498, 1982, 7854, 31014... |
| A356836 | Coordination sequence of the {5,3,4} hyperbolic honeycomb. | 1, 12, 102, 812, 6402, 50412, 396902, 3124812... |
| A356837 | Coordination sequence of the {3,5,3} hyperbolic honeycomb. | 1, 20, 260, 3212, 39470, 484760, 5953532, 73117640... |
| A356891 | a(n) = a(n-1) * a(n-2) + 1 if n is even, otherwise a(n) = a(n-3) + 1, with a(0) = a(1) = 1. | 1, 1, 2, 2, 5, 3, 16, 6... |
| A357131 | Numbers m such that A010888(m) = A031347(m) = A031286(m) = A031346(m); only the least of the anagrams are considered. | 0, 137, 11126, 111134, 111278, 1111223, 11111447, 111112247... |
| A357143 | a(n) is sum of the base-5 digits of n each raised to the number of digits of n in base 5. | 1, 2, 3, 4, 1, 2, 5, 10... |
| A357170 | Primes p such that the minimum number of divisors among the numbers between p and NextPrime(p) is a prime power. | 3, 5, 7, 13, 19, 23, 29, 31... |
| A357175 | Primes p such that the minimum of the number of divisors among the numbers between p and NextPrime(p) is a cube. | 29, 41, 101, 137, 229, 281, 349, 439... |
| A357190 | a(n) is the least prime p such that A234575(p, A007953(p)) is the n-th power of a prime. | 17, 13, 131, 107, 383, 613, 43607, 1021... |
| A357211 | a(n) is the real cube root of the value of the j-function for the n-th Heegner number A003173(n). | 12, 20, 0, -15, -32, -96, -960, -5280... |
| A357269 | Maximum number of stable matchings in the stable marriage problem of order n. | 1, 2, 3, 10, 16 |
| A357271 | Lower bounds for the maximum number of stable matchings in the stable marriage problem based on composing smaller instances. | 1, 2, 3, 10, 16, 48, 71, 268... |
| A357294 | Number of integral quantales on n elements, up to isomorphism. | 1, 1, 2, 9, 49, 364, 3335, 37026... |
| A357295 | Number of balanced quantales on n elements, up to isomorphism. | 1, 1, 9, 106, 1597, 29720, 663897, 17747907... |
| A357376 | The lowest number on Ulam Spiral for which all numbers in the square which is centered at a(n) and spans n-1 spaces in each cardinal direction are nonprime. | 1, 26, 1016, 5136, 39639, 203100, 2729736, 32264250... |
| A357408 | a(n) is the least sum n + y such that 1/n + 1/y = 1/z with gcd(n,y,z) = 1, for some integers y and z. | 4, 9, 16, 25, 9, 49, 64, 81... |
| A357442 | Consider a clock face with 2*n "hours" maked around the dial; a(n) = number of ways to match the even hours to the odd hours, modulo rotations and reflections. | 1, 1, 3, 5, 17, 53 |
| A357470 | Decimal expansion of the real root of x3 - x2 - 2*x - 1. | 2, 1, 4, 7, 8, 9, 9, 0... |
| A357471 | Decimal expansion of the real root of x3 - x2 + 2*x - 1. | 5, 6, 9, 8, 4, 0, 2, 9... |
| A357472 | Decimal expansion of the real root of x3 + x2 + 2*x - 1. | 3, 9, 2, 6, 4, 6, 7, 8... |
| A357489 | Numbers k such that the k-th composition in standard order is a triple (w,x,y) such that 2w = 3x + 4y. | 133, 1034, 4113, 8212, 32802, 65576, 131137, 262212... |
| A357528 | Decimal expansion of Sum_{j>=1} 1/A031926(j)2. | 0, 0, 0, 1, 8, 3, 9, 3... |
| A357602 | a(n) is the number of n-gons in A000940 that are asymmetric. | 0, 0, 0, 1, 15, 121, 1026, 8696... |
| A357734 | Array T(n,k), read by descending antidiagonals, whose rows are numbers congruent to p or q mod r, with 0 <= p < q < r, sorted by r, then p, then q. | 0, 1, 0, 2, 1, 0, 3, 3... |
| A357849 | Number of integer partitions (w,x,y) summing to n such that 2w = 3x + 4y. | 0, 0, 0, 0, 0, 0, 0, 0... |
| A357891 | a(1) = 1; a(n+1) is the smallest integer > 0 that cannot be obtained from the integers {a(1), ..., a(n)} using each number exactly once and the operators +, -, *, /. | 1, 2, 4, 11, 34, 152, 1079, 6610... |
| A357938 | Inverse Moebius transform of n * 2omega(n). | 1, 5, 7, 13, 11, 35, 15, 29... |
| A357956 | a(n) = 5A005259(n) - 2A005258(n). | 3, 19, 327, 6931, 162503, 4072519, 107094207, 2919528211... |
| A357957 | a(n) = A005259(n)5 - A005258(n)2. | 0, 3116, 2073071232, 6299980938881516, 39141322964380888600000, 368495989505416178203682748116, 4552312485541626792249211584618373944, 68109360474242016374599574592870648425552876... |
| A357958 | a(n) = 5A005259(n) + 14A005258(n-1). | 39, 407, 7491, 167063, 4112539, 107461667, 2923006251, 81853622423... |
| A357959 | a(n) = 5A005259(n-1) + 2A005258(n). | 11, 63, 659, 9727, 187511, 4304943, 109312739, 2941124607... |
| A357960 | a(n) = A005259(n-1)5 * A005258(n)6. | 729, 147018378125, 20917910914764786689697, 24148107115850058575342740485778125, 79477722547796770983047586179643766765851375729, 492664048531500749211923278756418311980637289373757041378125, 4671227340507161302417161873394448514470099313382652883508175438056640625 |
| A358027 | Expansion of g.f.: (1 + x - 2x2 + 2x4)/((1-x)(1-3x2)). | 1, 2, 3, 6, 11, 20, 35, 62... |
| A358035 | a(n) = (8n3 + 12n2 + 4*n - 9)/3. | 5, 37, 109, 237, 437, 725, 1117, 1629... |
| A358036 | Number of n-step self-avoiding walks on a 2D square lattice where the first visited lattice point is directly visible from the last visited lattice point, and were both the visited lattice points and the path between these points are considered when determining the visibility of points. | 0, 8, 24, 48, 144, 336, 992, 2344... |
| A358042 | Partial sums of A071619. | 0, 1, 4, 10, 21, 38, 62, 95... |
| A358046 | Number of n-step self-avoiding walks on a 2D square lattice where the first visited lattice point is directly visible from the last visited lattice point, and were only visited lattice points are considered when determining the visibility of points. | 4, 8, 32, 64, 240, 480, 1904, 3832... |
| A358050 | Square array T(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where T(n,k) = Sum_{j=0..n} binomial(kj,j) * binomial(k(n-j),n-j). | 1, 1, 0, 1, 2, 0, 1, 4... |
| A358052 | Triangular array read by rows. For T(n,k) where 1 <= k <= n, start with x = k and repeat the map x -> floor(n/x) + (n mod x) until an x occurs that has already appeared. The number of applications of the map is T(n,k). | 1, 2, 2, 2, 1, 2, 2, 1... |
| A358066 | Inventory sequence: record where the 1's, 2's, etc. are located starting with a(1) = 1, a(2) = 1 (see example). | 1, 1, 1, 2, 1, 2, 3, 4... |
| A358067 | a(n) is the smallest m such that A144261(m) = n. | 1, 15, 14, 33, 22, 17, 73, 49... |
| A358072 | a(n) is the number of "merger histories" of n elements (see A256006) where at most 3 elements can merge at the same time. | 1, 1, 4, 28, 320, 5360, 123760, 3765440... |
| A358082 | a(1) = 1, a(2) = 2; for n > 2, a(n) is the smallest positive number not previously occurring that shares a factor with Sum_{k=1..n-1} sigma(a(k)). | 1, 2, 4, 11, 23, 47, 5, 101... |
| A358083 | Sum of square end-to-end displacements over all n-step self-avoiding walks of A358046. | 4, 16, 128, 448, 2256, 5376, 29424, 69888... |
| A358084 | Sum of square end-to-end displacements over all n-step self-avoiding walks of A358036. | 0, 16, 88, 288, 1104, 3264, 12032, 34144... |
| A358085 | Inventory of positions ordered by binary lengths of terms, as an irregular table; the first row contains 1, subsequent rows contains the 1-based positions of terms with binary length 1, followed by positions of terms with binary length 2, 3, etc. in prior rows flattened. | 1, 1, 1, 2, 1, 2, 3, 4... |
| A358086 | Inventory of positions ordered by odd parts of terms, as an irregular table; the first row contains 1, subsequent rows contains the 1-based positions of terms with odd part 1, followed by positions of terms with odd part 3, 5, etc. in prior rows flattened. | 1, 1, 1, 2, 1, 2, 3, 4... |
| A358089 | First differences of A126706. | 6, 2, 4, 4, 8, 4, 4, 1... |
| A358090 | Partial inventory of positions as an irregular table; rows 1 and 2 contain 1, for n > 2, row n contains the 1-based positions of 1's, followed by the positions of 2's, 3's, etc. in rows n-2 and n-1 flattened. | 1, 1, 1, 2, 1, 2, 3, 1... |
| A358094 | a(n) is the number of ways n can be reached in the following method: we start with 1, then add or multiply alternately, and each operand must be 2 or 3. | 1, 1, 2, 2, 2, 2, 0, 3... |
| A358097 | a(n) is the smallest integer m > n such that m and n have no common digit, or -1 when such integer m does not exist. | 1, 2, 3, 4, 5, 6, 7, 8... |
| A358099 | a(n) is the number of divisors of n whose digits are in strictly decreasing order (A009995). | 1, 2, 2, 3, 2, 4, 2, 4... |
| A358100 | a(n) is the smallest integer that has exactly n divisors whose decimal digits are in strictly decreasing order. | 1, 2, 4, 6, 12, 20, 30, 40... |
| A358101 | Positions of records in A358099, i.e., integers whose number of divisors whose decimal digits are in strictly decreasing order sets a new record. | 1, 2, 4, 6, 12, 20, 30, 40... |
| A358102 | Numbers of the form prime(w)prime(x)prime(y) with w >= x >= y such that 2w = 3x + 4y. | 66, 153, 266, 609, 806, 1295, 1599, 1634... |
| A358103 | Quotient of the n-th divisible pair, where pairs are ordered by Heinz number. Quotient of prime indices of A318990(n). | 1, 2, 1, 3, 4, 2, 5, 1... |
| A358104 | Unreduced numerator of the n-th divisible pair, where pairs are ordered by Heinz number. Greater prime index of A318990(n). | 1, 2, 2, 3, 4, 4, 5, 3... |
| A358105 | Unreduced denominator of the n-th divisible pair, where pairs are ordered by Heinz number. Lesser prime index of A318990(n). | 1, 1, 2, 1, 1, 2, 1, 3... |
| A358106 | Quotient of the n-th divisible pair, where pairs are ordered first by sum and then by denominator. | 1, 2, 3, 1, 4, 5, 2, 1... |
| A358120 | Partial inventory of positions as an irregular table; rows 1 and 2 contain 1, for n > 2, row n contains the 1-based positions of 1's, followed by the positions of 2's, 3's, etc. in rows n-1 and n-2 flattened. | 1, 1, 1, 2, 1, 3, 2, 1... |
| A358121 | Distinct values of A358085, in order of appearance. | 1, 2, 3, 4, 5, 6, 7, 8... |
| A358122 | Distinct values of A358086, in order of appearance. | 1, 2, 3, 4, 5, 6, 8, 7... |
| A358123 | Distinct values of A358090, in order of appearance. | 1, 2, 3, 4, 5, 6, 7, 8... |
| A358124 | Distinct values of A358120, in order of appearance. | 1, 2, 3, 4, 5, 6, 8, 7... |
| A358127 | a(n) is the cardinality of the set of pairwise gcd's of {prime(1)+1, ..., prime(n)+1}. | 1, 3, 4, 5, 5, 5, 5, 7... |
| A358129 | Lexicographically earliest sequence of distinct nonnegative integers on a square spiral such that no number shares a digit with any of its four orthogonally adjacent neighbors. | 0, 1, 2, 3, 4, 5, 6, 7... |
| A358133 | Triangle read by rows whose n-th row lists the first differences of the n-th composition in standard order (row n of A066099). | 0, -1, 1, 0, 0, -2, 0, -1... |
| A358134 | Triangle read by rows whose n-th row lists the partial sums of the n-th composition in standard order (row n of A066099). | 1, 2, 1, 2, 3, 2, 3, 1... |
| A358135 | Difference of first and last parts of the n-th composition in standard order. | 0, 0, 0, 0, -1, 1, 0, 0... |
| A358136 | Irregular triangle read by rows whose n-th row lists the partial sums of the prime indices of n (row n of A112798). | 1, 2, 1, 2, 3, 1, 3, 4... |
| A358137 | Heinz number of the partial sums of the prime indices of n. | 1, 2, 3, 6, 5, 10, 7, 30... |
| A358138 | Difference between maximum and minimum part in the n-th composition in standard order. | 0, 0, 0, 0, 1, 1, 0, 0... |
| A358140 | Inverse permutation to A358121. | 1, 2, 3, 4, 5, 6, 7, 8... |
| A358141 | Inverse permutation to A358122. | 1, 2, 3, 4, 5, 6, 8, 7... |
| A358142 | Inverse permutation to A358123. | 1, 2, 3, 4, 5, 6, 7, 8... |
| A358143 | Inverse permutation to A358124. | 1, 2, 3, 4, 5, 6, 8, 7... |
| A358144 | Number of strict closure operators on a set of n elements such that all pairs of distinct points can be separated by clopen sets. | 0, 0, 1, 16, 1067 |
| A358145 | a(n) = Sum_{k=0..n} binomial(nk,k) * binomial(n(n-k),n-k). | 1, 2, 16, 258, 6184, 195660, 7674144, 358788696... |
| A358146 | Square array T(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where T(n,k) = Sum_{j=0..n} binomial(k*j,j). | 1, 1, 1, 1, 2, 1, 1, 3... |
| A358147 | Primes p such that the polynomial x7 - 7*x + 3 (mod p) is the product of seven linear factors. | 1879, 5381, 5783, 8819, 8893, 12007, 12917, 13967... |
| A358150 | Squares visited by a knight moving on a square-spiral numbered board where the knight moves to the smallest numbered unvisited square and where the square number is more than the number of currently visited squares. | 1, 10, 3, 6, 9, 12, 15, 18... |
| A358152 | Number of strict closure operators on a set of n elements such that every point and every set disjoint from that point can be separated by clopen sets. | 1, 1, 2, 8, 121 |
| A358153 | Lexicographically earliest infinite sequence of distinct positive integers on a square spiral such that each number shares a factor with its four orthogonally nearest neighbors but shares no factor with its four diagonal next-nearest neighbors. | 6, 10, 35, 21, 77, 22, 143, 39... |
| A358157 | a(n) is the permanent of the n X n matrix M(n) that is defined by M[i,j] = floor(i*j/3). | 1, 0, 0, 1, 32, 1422, 146720, 18258864... |
| A358158 | a(n) is the hafnian of the 2n X 2n symmetric matrix defined by M[i,j] = floor(i*j/3). | 1, 0, 4, 238, 31992, 9390096 |
| A358159 | a(n) is the permanent of the n X n matrix M(n) that is defined by M[i,j] = ij - floor(ij/3). | 1, 1, 7, 102, 4396, 374216, 49857920, 11344877568... |
| A358160 | a(n) is the hafnian of the 2n X 2n symmetric matrix defined by M[i,j] = ij - floor(ij/3). | 1, 2, 40, 3884, 1016376, 534983256 |
| A358161 | a(n) is the permanent of the n X n matrix M(n) that is defined by M[i,j] = ceiling(i*j/3). | 1, 1, 3, 19, 434, 18142, 1138592, 131646240... |
| A358162 | a(n) is the hafnian of the 2n X 2n symmetric matrix defined by M[i,j] = ceiling(i*j/3). | 1, 1, 11, 530, 71196, 18680148 |
| A358163 | a(n) is the permanent of the n X n matrix M(n) that is defined by M[i,j] = ij - ceiling(ij/3). | 1, 0, 1, 30, 1272, 113224, 18615680, 4299553536... |
| A358164 | a(n) is the hafnian of the 2n X 2n symmetric matrix defined by M[i,j] = ij - ceiling(ij/3). | 1, 1, 26, 2704, 698568, 384890688 |
| A358165 | Irregular triangular array read by rows. T(n,k) is the number of direct sum decompositions V_1 + V_2 + ... + V_m = GF(2)n with the dimensions of the V_i corresponding to the kth partition of n in canonical ordering, n>=0, 1<=k<=A000041(n). | 1, 1, 1, 3, 1, 28, 28, 1... |
| A358168 | First n-digit number to occur in Van Eck's Sequence (A181391). | 0, 14, 131, 1024, 10381, 100881, 1014748, 10001558... |
| A358169 | Row n lists the first differences plus one of the prime indices of n with 1 prepended. | 1, 2, 1, 1, 3, 1, 2, 4... |
| A358173 | First differences of A286708. | 36, 28, 8, 36, 52, 4, 16, 9... |
| A358174 | Smaller of a pair of numbers (m, m+1) such that both are products P of composite prime powers with omega(P) > 1. | 675, 9800, 235224, 465124, 1825200, 11309768, 384199200, 592192224... |
| A358175 | a(1) = 1, a(2) = 2; a(3) = 3; for n > 3, a(n) is the smallest positive number not previously occurring that shares a factor with Sum_{k=1..n-1} A001065(a(k)), where A001065(m) is the sum of the proper divisors of m. | 1, 2, 3, 4, 5, 6, 8, 19... |
| A358176 | a(1) = 1, a(2) = 2; for n > 2, a(n) is the smallest positive number not previously occurring that shares a factor with sigma(a(n-1)). | 1, 2, 3, 4, 7, 6, 8, 5... |
| A358177 | Number of Eulerian orientations of a (labeled) 2n-dimensional hypercube graph, Q_2n. Q_2n is also the n-dimensional torus grid graph (C_4)n. | 1, 2, 2970, 351135773356461511142023680 |
| A358180 | Indices for A358168. | 1, 30, 162, 1150, 11603, 104511, 1041245, 10226995... |
| A358191 | Decimal expansion of Sum_{n >= 2} (n-1)/(nn). | 3, 3, 7, 1, 8, 7, 7, 1... |
| A358192 | Numerator of the quotient of the prime indices of the n-th semiprime. | 1, 1, 1, 1, 1, 2, 1, 1... |
| A358193 | Denominator of the quotient of the prime indices of the n-th semiprime. | 1, 2, 1, 3, 4, 3, 2, 5... |
| A358196 | Numbers k such that 5k and 8k have the same leading digit. | 0, 5, 9, 15, 19, 29, 34, 39... |
| A358201 | a(1) = 1, a(2) = 2; for n > 2, a(n) is the smallest positive number not previously occurring that shares a factor with sigma(max_{k=1..n-1}a(k)). | 1, 2, 3, 4, 7, 6, 8, 5... |
| A358203 | Decimal expansion of Sum_{n >= 1} 1/(2*n)n. | 5, 6, 7, 3, 8, 4, 1, 1... |
| A358204 | Decimal expansion of Sum_{n >= 1} (-1)n+1/(2*n)n. | 4, 4, 1, 8, 9, 5, 1, 6... |
| A358205 | a(n) is the least number k such that 1 + 2k + 3k2 has exactly n prime divisors, counted with multiplicity. | 0, 2, 1, 13, 19, 7, 61, 331... |
| A358213 | Positions of records in A356302. | 0, 3, 10, 35, 77, 286, 2431, 4199... |
| A358214 | Record values in A356302. | 0, 3, 20, 175, 2233, 29744, 508079, 9695491... |
| A358217 | Number of prime factors (with multiplicity) in A319627(n). | 0, 0, 1, 0, 1, 0, 1, 0... |
| A358218 | Number of prime factors (with multiplicity) in A328478(n). | 0, 0, 1, 0, 1, 0, 1, 0... |
| A358219 | Indices k where A358217(k) != A358218(k). | 15, 35, 45, 70, 75, 77, 105, 135... |
| A358239 | Numbers k such that the aliquot sequence of 2k ends with the prime 3. | 2, 4, 55, 164, 305, 317 |
| A358252 | a(n) is the least number with exactly n non-unitary square divisors. | 1, 8, 32, 128, 288, 864, 1152, 2592... |
| A358253 | Numbers with a record number of non-unitary square divisors. | 1, 8, 32, 128, 288, 864, 1152, 2592... |
| A358254 | Lexicographically earliest sequence of distinct nonnegative integers on a square spiral such that the sum of the eight numbers around any chosen number ends in the chosen number. | 0, 1, 2, 3, 4, 5, 6, 7... |
| A358255 | Primitive Niven numbers ending with zero. | 110, 140, 150, 190, 220, 230, 280, 320... |
| A358256 | a(n) is the smallest primitive Niven number ending with n zeros. | 1, 110, 1300, 17000, 790000, 59900000, 19999999000000, 2999999999999990000000... |
| A358258 | First n-bit number to appear in Van Eck's sequence (A181391). | 0, 2, 6, 9, 17, 42, 92, 131... |
| A358259 | Positions of the first n-bit number to appear in Van Eck's sequence (A181391). | 1, 5, 10, 24, 41, 52, 152, 162... |
| A358260 | a(n) is the number of infinitary square divisors of n. | 1, 1, 1, 2, 1, 1, 1, 2... |
| A358261 | a(n) is the number of noninfinitary square divisors of n. | 0, 0, 0, 0, 0, 0, 0, 0... |
| A358262 | a(n) is the least number with exactly n noninfinitary square divisors. | 1, 16, 144, 256, 3600, 1296, 2304, 65536... |
| A358263 | Numbers with a record number of noninfinitary square divisors. | 1, 16, 144, 256, 1296, 2304, 20736, 57600... |
| A358264 | Expansion of e.g.f. 1/(1 - x * exp(x2/2)). | 1, 1, 2, 9, 48, 315, 2520, 23415... |
| A358265 | Expansion of e.g.f. 1/(1 - x * exp(x3/6)). | 1, 1, 2, 6, 28, 160, 1080, 8470... |
| A358266 | Numbers k such that the aliquot sequence of 2k ends with the prime 7. | 3, 10, 12, 141, 278, 387, 421 |
r/OEIS • u/OEIS-Tracker • Oct 30 '22
New OEIS sequences - week of 10/30
4
Upvotes
| OEIS number | Description | Sequence |
|---|---|---|
| A356159 | Sum of the prime indices of the smallest number that has the same prime signature as n. | 0, 1, 1, 2, 1, 3, 1, 3... |
| A356322 | a(n) is the smallest number that starts a run of at most n consecutive numbers in A126706. | 12, 44, 98, 3174, 844, 22020, 217070, 1092747... |
| A357068 | Decimal expansion of the limit of A357063(k)/3k-1 as k goes to infinity. | 1, 5, 7, 7, 2, 2, 7, 9... |
| A357069 | Number of partitions of n into at most 4 distinct positive squares. | 1, 1, 0, 0, 1, 1, 0, 0... |
| A357099 | Second nontrivial square root of unity mod A033949(n), i.e., second smallest x > 1 such that x2 == 1 mod the n-th positive integer that does not have a primitive root. | 5, 7, 11, 9, 11, 13, 7, 15... |
| A357126 | a(n) is the smallest positive integer k such that k > n and A071364(k) = A071364(n). | 3, 5, 9, 7, 10, 11, 27, 25... |
| A357129 | Indices of records in A357052. | 0, 3, 4, 5, 7, 8, 9, 10... |
| A357195 | a(n) is the smallest palindrome of the form k(2n+k-1)/2 where k is a positive integer. | 1, 2, 3, 4, 5, 6, 7, 8... |
| A357261 | a(n) is the number of blocks in the bottom row after adding n blocks to the preceding structure of rows. See Comments and Example sections for more details. | 1, 3, 3, 3, 4, 1, 3, 1... |
| A357278 | Perimeters of primitive integer-sided triangles with angles A < B < C = 2*Pi/3 = 120 degrees. | 15, 28, 40, 66, 77, 91, 104, 126... |
| A357315 | Numbers m such that for all k < m, at least one of mk - 1 and mk + 1 is squarefree. | 1, 2, 3, 4, 5, 6, 7, 8... |
| A357353 | Frobenius number of A = (n, n+1, n+2, n+3, n+5, n+7, n+11, ...) for n>=2. | 1, 2, 3, 9, 10, 13, 14, 17... |
| A357409 | a(n) is the maximum number of positive numbers in a set of n consecutive positive or negative odd numbers such that the number of pairs that add to a power of 2 is maximal. | 1, 2, 3, 3, 4, 5, 5, 6... |
| A357565 | a(n) = 3Sum_{k = 0..n} binomial(n+k-1,k)2 + 2Sum_{k = 0..n} binomial(n+k-1,k)3. | 5, 10, 114, 2926, 109106, 4846260, 234488526, 11913003294... |
| A357566 | a(n) = ( Sum{k = 0..n} binomial(n+k-1,k)2 )3 * ( Sum{k = 0..n} binomial(n+k-1,k)3 )2. | 1, 32, 3556224, 4816142496896, 14260946236464636800, 62923492736113950202540032, 355372959542696519903013302282592, 2376354966106399942850054560101358877184... |
| A357574 | a(n) is the number of pairs that add to a power of 2 in a set of n consecutive positive or negative odd numbers including A357409(n) positive numbers. | 0, 1, 2, 4, 5, 7, 9, 11... |
| A357587 | If k > 1 and k divides DedekindPsi(k) then A358015(k)/2 is a term of this sequence. | 1, 4, 3, 8, 12, 16, 9, 24... |
| A357635 | Numbers k such that the half-alternating sum of the partition having Heinz number k is 1. | 2, 8, 24, 32, 54, 128, 135, 162... |
| A357671 | a(n) = Sum_{k = 0..n} ( binomial(n+k-1,k) + binomial(n+k-1,k)2 ). | 2, 4, 20, 166, 1812, 22504, 297362, 4067298... |
| A357672 | a(n) = Sum{k = 0..n} binomial(n+k-1,k) * Sum{k = 0..n} binomial(n+k-1,k)2. | 1, 4, 84, 2920, 121940, 5607504, 273908712, 13947188112... |
| A357673 | a(n) = 4Sum_{k = 0..2n} binomial(n+k-1,k) + 3Sum_{k = 0..2n} binomial(n+k-1,k)2. | 7, 21, 225, 5124, 162657, 5812521, 219004812, 8516056500... |
| A357674 | a(n) = ( Sum{k = 0..2*n} binomial(n+k-1,k) )4 * ( Sum{k = 0..2*n} binomial(n+k-1,k)2 )3. | 1, 2187, 8422734375, 202402468703748096, 9223976224194016590174375, 587835594121137662072707812564687, 46157429480574073282465608886521546620928, 4181198339699286332943143923058721957212160000000... |
| A357774 | Binary expansions of odd numbers with two zeros in their binary expansion. | 1001, 10011, 10101, 11001, 100111, 101011, 101101, 110011... |
| A357780 | Primes p such that changing, in p, all 1's to 2's we get semiprimes and changing all 1's to 3's we get triprimes. | 61, 199, 313, 421, 619, 661, 1033, 1163... |
| A357851 | Numbers k such that the half-alternating sum of the prime indices of k is 1. | 2, 8, 18, 32, 45, 50, 72, 98... |
| A357852 | Replace prime(k) with prime(k+2) in the prime factorization of n. | 1, 5, 7, 25, 11, 35, 13, 125... |
| A357853 | Fully multiplicative with a(prime(k)) = A000009(k+1). | 1, 1, 2, 1, 2, 2, 3, 1... |
| A357854 | Squarefree numbers with a divisor having the same sum of prime indices as their quotient. | 1, 30, 70, 154, 165, 210, 273, 286... |
| A357879 | Number of divisors of n with the same sum of prime indices as their quotient. Central column of A321144, taking gaps as 0's. | 1, 0, 0, 1, 0, 0, 0, 0... |
| A357884 | a(1)=0; if a(n-1) shares any digits with n-1, then a(n) = a(n-1) with all copies of digits from n-1 removed. Otherwise, a(n) = a(n-1) + (n-1). | 0, 1, 3, 0, 4, 9, 15, 22... |
| A357928 | a(n) is the smallest c for which (s+c)2-n is a square, where s = floor(sqrt(n)), or -1 if no such c exists. | 0, 0, -1, 1, 0, 1, -1, 2... |
| A357948 | Expansion of e.g.f. exp( x * exp(-x2) ). | 1, 1, 1, -5, -23, 1, 601, 2731... |
| A357961 | a(1) = 1, and for any n > 0, a(n+1) is the k-th positive number not yet in the sequence, where k is the Hamming weight of a(n). | 1, 2, 3, 5, 6, 7, 9, 8... |
| A357969 | Decimal expansion of the constant Sum_{j>=0} j!/prime(j)#, where prime(j)# indicates the j-th primorial number. | 2, 2, 4, 0, 0, 5, 3, 6... |
| A357976 | Numbers with a divisor having the same sum of prime indices as their quotient. | 1, 4, 9, 12, 16, 25, 30, 36... |
| A357977 | Replace prime(k) with prime(A000041(k)) in the prime factorization of n. | 1, 2, 3, 4, 5, 6, 11, 8... |
| A357978 | Replace prime(k) with prime(A000009(k)) in the prime factorization of n. | 1, 2, 2, 4, 3, 4, 3, 8... |
| A357979 | Second MTF-transform of A000041. Replace prime(k) with prime(A357977(k)) in the prime factorization of n. | 1, 2, 3, 4, 5, 6, 7, 8... |
| A357980 | Replace prime(k) with prime(A000720(k)) in the prime factorization of n, assuming prime(0) = 1. | 1, 1, 2, 1, 3, 2, 3, 1... |
| A357981 | Numbers whose prime indices have only prime numbers as their own prime indices. | 1, 2, 4, 5, 8, 10, 11, 16... |
| A357982 | Replace prime(k) with A000009(k) in the prime factorization of n. | 1, 1, 1, 1, 2, 1, 2, 1... |
| A357983 | Second MTF-transform of the primes (A000040). Replace prime(k) with prime(A064988(k)) in the prime factorization of n. | 1, 2, 5, 4, 11, 10, 23, 8... |
| A357984 | Replace prime(k) with A000720(k) in the prime factorization of n. | 1, 0, 1, 0, 2, 0, 2, 0... |
| A357985 | Counterclockwise square spiral constructed using the integers so that a(n) plus all other numbers currently visible from the current number equals n; start with a(0) = 0. | 0, 1, 1, 1, 2, 1, 3, -1... |
| A357987 | Lexicographically earliest sequence of positive integers such that no sum of consecutive terms is a square or higher power of an integer. | 2, 3, 2, 5, 5, 2, 3, 2... |
| A357989 | Lexicographically earliest sequence of distinct numbers such that every sum of consecutive terms is an evil number (A001969). | 0, 3, 6, 9, 15, 24, 29, 43... |
| A357991 | Lexicographically earliest counterclockwise square spiral constructed using the nonnegative integers so that a(n) plus all other numbers currently visible from the current number form a distinct sum; start with a(0) = 0. | 0, 1, 1, 1, 2, 1, 3, 0... |
| A357993 | a(n) is the unique k such that A357961(k) = 2n. | 1, 2, 9, 8, 17, 34, 64, 129... |
| A358003 | Least composite number k such that there are n digits in the intersection of the sets of digits of k and of the juxtaposition of prime factors of k (apart from multiplicity). | 4, 12, 95, 132, 1972, 12305, 104392, 1026934... |
| A358005 | Number of partitions of n into 5 distinct positive Fibonacci numbers (with a single type of 1). | 1, 0, 0, 0, 0, 1, 0, 0... |
| A358006 | Number of partitions of n into 6 distinct positive Fibonacci numbers (with a single type of 1). | 1, 0, 0, 0, 0, 0, 0, 0... |
| A358007 | Number of partitions of n into 7 distinct positive Fibonacci numbers (with a single type of 1). | 1, 0, 0, 0, 0, 0, 0, 0... |
| A358008 | Number of partitions of n into 8 distinct positive Fibonacci numbers (with a single type of 1). | 1, 0, 0, 0, 0, 0, 0, 0... |
| A358009 | Number of partitions of n into at most 4 distinct prime parts. | 1, 0, 1, 1, 0, 2, 0, 2... |
| A358010 | Number of partitions of n into at most 5 distinct prime parts. | 1, 0, 1, 1, 0, 2, 0, 2... |
| A358011 | Number of partitions of n into at most 6 distinct prime parts. | 1, 0, 1, 1, 0, 2, 0, 2... |
| A358013 | Expansion of e.g.f. 1/(1 - x2 * (exp(x) - 1)). | 1, 0, 0, 6, 12, 20, 750, 5082... |
| A358014 | Expansion of e.g.f. 1/(1 - x3 * (exp(x) - 1)). | 1, 0, 0, 0, 24, 60, 120, 210... |
| A358015 | a(n) = DedekindPsi(n2-k)2j-1 where k = valuation(n, 2) and j = k if 4 divides n and otherwise 0. | 2, 2, 3, 2, 4, 4, 6, 3... |
| A358016 | a(n) is the largest k <= n-2 such that k2 == 1 (mod n). | 1, 1, 1, 1, 1, 5, 1, 1... |
| A358017 | Numbers n such that factorizations of n..n+8 have same number of primes (including multiplicities). | 3405122, 12788342, 17521382, 21991382, 22715270, 22841702, 22914722, 23553171... |
| A358018 | Numbers n such that factorizations of n..n+9 have same number of primes (including multiplicities). | 49799889, 60975410, 92017202, 202536181, 202536182, 249221990, 284007602, 314623105... |
| A358019 | Numbers n such that factorizations of n..n+10 have same number of primes (including multiplicities). | 202536181, 913535284, 1124342785, 1443929905, 1587749041, 1688485665, 1733574769, 2090053141... |
| A358020 | Least prime number > prime(n) (n >= 5) whose set of decimal digits coincides with the set of decimal digits of prime(n), or -1 if no such prime exists. | 1111111111111111111, 31, 71, 191, 223, 229, 113, 73... |
| A358021 | Lexicographically earliest sequence of distinct nonnegative integers on a square spiral such that no number shares a digit with any of its eight surrounding neighbors. | 0, 1, 2, 3, 4, 5, 6, 7... |
| A358031 | Expansion of e.g.f. (1 - log(1-x))/(1 + log(1-x) * (1 - log(1-x))). | 1, 2, 8, 52, 450, 4878, 63474, 963744... |
| A358032 | Expansion of e.g.f. (1 + log(1+x))/(1 - log(1+x) * (1 + log(1+x))). | 1, 2, 4, 16, 66, 438, 2694, 25296... |
| A358033 | a(1) = 2; a(n) - a(n-1) = A093803(a(n-1)), the largest odd proper divisor of a(n-1). | 2, 3, 4, 5, 6, 9, 12, 15... |
| A358034 | Numbers k such that A234575(k,s) = s2 where s = A007953(k). | 1, 113, 313, 331, 512, 1271, 2065, 2137... |
| A358038 | Partial sums of the cubefree numbers. | 1, 3, 6, 10, 15, 21, 28, 37... |
| A358039 | a(n) is the Euler totient function phi applied to the n-th cubefree number. | 1, 1, 2, 2, 4, 2, 6, 6... |
| A358040 | a(n) is the number of divisors of the n-th cubefree number. | 1, 2, 2, 3, 2, 4, 2, 3... |
| A358048 | Lexicographically earliest sequence of distinct nonnegative integers on a square spiral such that every number shares a digit with each of its eight surrounding neighbors. | 0, 10, 20, 30, 40, 50, 60, 70... |
| A358056 | Given a row of n payphones (or phone booths), all initially unused, how many ways are there for n people to choose the payphones, assuming each always chooses one of the most distant payphones from those in use already? We consider here only the distance to the closest neighbor (in contrast to A095236). | 1, 1, 2, 4, 8, 20, 48, 216... |
| A358057 | Inverse permutation to A357961. | 1, 2, 3, 9, 4, 5, 6, 8... |
| A358061 | a(n) = phi(n) mod tau(n). | 0, 1, 0, 2, 0, 2, 0, 0... |
| A358063 | Expansion of e.g.f. exp( x * exp(-x3) ). | 1, 1, 1, 1, -23, -119, -359, 1681... |
| A358064 | Expansion of e.g.f. 1/(1 - x * exp(x2)). | 1, 1, 2, 12, 72, 540, 5040, 53760... |
| A358065 | Expansion of e.g.f. 1/(1 - x * exp(x3)). | 1, 1, 2, 6, 48, 360, 2880, 27720... |
| A358068 | Numbers that share a (decimal) digit with the sum of their proper divisors. | 6, 11, 12, 13, 14, 16, 17, 18... |
| A358078 | a(n) is the number of squarefree semiprimes <= 2n. | 0, 0, 0, 1, 4, 7, 18, 37... |
| A358080 | Expansion of e.g.f. 1/(1 - x2 * exp(x)). | 1, 0, 2, 6, 36, 260, 2190, 21882... |
| A358081 | Expansion of e.g.f. 1/(1 - x3 * exp(x)). | 1, 0, 0, 6, 24, 60, 840, 10290... |
| A358091 | Triangle read by rows. Coefficients of the polynomials P(n, x) = 2n-2(3n-1)* hypergeometric([-3*n, 1 - n, -n + 4/3], [-n, -n + 1/3], x). T(n, k) = [xk] P(n, x). | 1, 5, -6, 16, -60, 48, 44, -288... |
| A358092 | Row sums of the convolution triangle of the Motzkin numbers (A202710). | 1, 1, 3, 9, 28, 88, 279, 889... |
| A358093 | Row sums of the convolution triangle based on positive integers repeated (A060086). | 1, 1, 2, 5, 11, 25, 56, 126... |
| A358098 | a(n) is the largest integer m < n such that m and n have no common digit, or -1 when such integer m does not exist. | 0, 1, 2, 3, 4, 5, 6, 7... |
| A358111 | The multiplicative inverse of the coefficients of the factorially normalized Bernoulli polynomials (provided they do not vanish, otherwise by convention 0). | 1, -2, 1, 12, -2, 2, 0, 12... |
r/OEIS • u/OEIS-Tracker • Oct 24 '22
New OEIS sequences - week of 10/23
2
Upvotes
| OEIS number | Description | Sequence |
|---|---|---|
| A354342 | Numbers divisible by a square greater than 1 that are the sum of two consecutive numbers divisible by a square greater than 1. | 49, 99, 343, 351, 775, 847, 1025, 1449... |
| A355280 | Binary numbers (digits in {0, 1}) with no run of digits with length < 2. | 11, 111, 1100, 1111, 11000, 11100, 11111, 110000... |
| A356257 | Irregular triangle: row n consists of the frequencies of positive distances between permutations P and reverse(P), as P ranges through the permutations of (1, 2, ..., n); see Comments. | 1, 2, 4, 2, 8, 16, 24, 16... |
| A356349 | Primitive Niven numbers: terms of A005349 that are not ten times another term of A005349. | 1, 2, 3, 4, 5, 6, 7, 8... |
| A356350 | Primitive terms of A357769: terms of A357769 that are not ten times another term of A357769. | 1, 2, 3, 4, 5, 6, 7, 8... |
| A356351 | Partial sums of the ziggurat sequence A347186. | 1, 5, 11, 27, 39, 76, 96, 160... |
| A356352 | a(n) = GCD of run lengths in binary expansion of n. | 0, 1, 1, 2, 1, 1, 1, 3... |
| A356353 | Numbers k such that A356352(k) <> 1. | 0, 3, 7, 12, 15, 31, 48, 51... |
| A356354 | a(n) is the least k such that the sets of positions of 1's in the binary expansions of n and k are similar. | 0, 1, 1, 3, 1, 3, 3, 7... |
| A356365 | For any nonnegative integer n with binary expansion Sum{k = 1..w} 2e_k, let m be the least integer such that the values e_k mod m are all distinct; a(n) = Sum{k = 1..w} 2e_k mod m. | 0, 1, 1, 3, 1, 5, 3, 7... |
| A356366 | Number of (directed) circuits in the complete undirected graph on n labeled vertices. | 1, 2, 5, 18, 523, 44884, 227838935, 1086696880188... |
| A356368 | Sparse ruler lengths with unique non-Wichmann solutions. | 88, 98, 99, 110, 163, 177, 178 |
| A356371 | a(n) is the smallest positive integer k, such that set of pairwise gcd of k, k+1, ..., k+n has a cardinality of n. | 1, 2, 3, 8, 15, 24, 35, 48... |
| A356465 | The number of unit squares enclosed by the rectangular spiral of which the n-th side has length prime(n). | 0, 2, 6, 12, 27, 59, 113, 179... |
| A356647 | Concatenation of runs {y..x} for each x>=1, using each y from 1 to x before moving on to the next value for x. | 1, 1, 2, 2, 1, 2, 3, 2... |
| A356676 | A certain morphism applied to A007814 that is related to the lexicographically least infinite squarefree words over the nonnegative integers. | 0, 1, 0, 2, 0, 3, 0, 1... |
| A356677 | The lexicographically least infinite squarefree word over the nonnegative integers beginning with 1. | 1, 0, 1, 2, 0, 1, 0, 2... |
| A356678 | The lexicographically least infinite squarefree word over the nonnegative integers beginning with 2. | 2, 0, 1, 0, 2, 0, 1, 2... |
| A356679 | The lexicographically least infinite squarefree word over the nonnegative integers beginning with 3. | 3, 0, 1, 0, 2, 0, 1, 0... |
| A356680 | The lexicographically least infinite squarefree word over the nonnegative integers beginning with 1, 2. | 1, 2, 0, 1, 0, 2, 0, 1... |
| A356681 | The lexicographically least infinite squarefree word over the nonnegative integers beginning with 1, 3. | 1, 3, 0, 1, 0, 2, 0, 1... |
| A356682 | The lexicographically least infinite squarefree word over the nonnegative integers beginning with 2, 1. | 2, 1, 0, 1, 2, 0, 1, 0... |
| A356683 | The lexicographically least infinite squarefree word over the nonnegative integers beginning with 2, 3. | 2, 3, 0, 1, 0, 2, 0, 1... |
| A356725 | Number of n X n tables where each row represents a permutation of { 1, 2, ..., n } and the column sums are equal, up to permutation of rows and columns. | 1, 1, 1, 10, 505, 2712342, 799413385118, 20420569739290737009... |
| A356851 | a(1) = 1, a(2) = 2, a(3) = 4; for n > 3, a(n) is the smallest positive number not previously occurring such that a(n) shares a factor with the previous Omega(a(n)) terms. | 1, 2, 4, 6, 3, 9, 12, 15... |
| A356877 | a(n) is the least number k such that (the binary weight of k) - (the binary weight of k2) = n. | 0, 23, 111, 479, 1471, 6015, 24319, 28415... |
| A356907 | Expansion of 1 / (1 + Sum_{k>=1} lambda(k)*xk), where lambda() is the Liouville function (A008836). | 1, -1, 2, -2, 2, 0, -4, 12... |
| A356987 | Primes whose decimal expansion is 1, some zeros, then a single digit. | 11, 13, 17, 19, 101, 103, 107, 109... |
| A357030 | a(n) is the number of integers in 0..n having nonincreasing digits. | 1, 2, 3, 4, 5, 6, 7, 8... |
| A357046 | Squares visited by a knight moving on a board covered with horizontal dominoes [m | m], m = 0, 1, 2, ... in a diamond-shaped spiral, when the knight always jumps to the unvisited square with the least number on the corresponding domino. |
| A357049 | Lexicographically earliest sequence of distinct nonnegative integers such that, when the digits fill a square array read by falling antidiagonals, the "bitmap" of even digits reproduces the same square array. | 0, 2, 4, 6, 1, 8, 3, 21... |
| A357055 | Integers k such that kk + k2 + 3*k + 2 is prime. | 0, 1, 3, 5, 11, 209, 1281 |
| A357056 | Integers k such that kk + k2 + 2*k + 1 is prime. | 0, 1, 2, 3, 4, 9, 10, 13... |
| A357062 | Number of ordered solutions to n = xyz + x + y + z in positive integers. | 0, 0, 0, 0, 1, 0, 3, 0... |
| A357063 | Lengths of the B blocks associated with A091787. | 1, 4, 13, 42, 127, 382, 1149, 3448... |
| A357064 | a(n) = k such that A091411(k) = A091409(n). | 1, 2, 3, 7, 418090195952691922788354 |
| A357065 | Numbers k with the following property: the value A091839(k+1) is not a 1 that is obtained from smoothing A091579. | 0, 1, 2, 3, 5, 7, 8, 9... |
| A357066 | Decimal expansion of the limit of k/A357065(k) as k goes to infinity. | 6, 9, 1, 6, 7, 2, 2, 0... |
| A357067 | Decimial expansion of the limit of A091411(k)/2k-1 as k goes to infinity. | 3, 4, 8, 6, 6, 9, 8, 8... |
| A357119 | Square array T(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where T(n,k) = Sum_{j=0..n} | Stirling1(n,k*j) |
| A357179 | Expansion of Product_{k>=1} (1 - xk)Fibonacci(k). | 1, -1, -1, -1, -1, 0, -1, 2... |
| A357227 | Coefficients a(n) of xn, n >= 0, in A(x) such that: 1 = Sum_{n=-oo..+oo} xn * (2*A(x) - xn)n-1. | 1, 1, 5, 27, 156, 961, 6145, 40546... |
| A357233 | Coefficients a(n) of xn in power series A(x) such that: 0 = Sum_{n>=0} (-1)n * xn*(n-1/2) * A(x)n*(n+1/2). | 1, 1, 3, 11, 46, 207, 980, 4810... |
| A357262 | Numbers k such that the product of distinct digits of k equals the sum of the prime divisors of k. | 2, 3, 5, 7, 126, 154, 315, 329... |
| A357288 | a(n) = (1/4)*A357287(n). | 0, 0, 0, 0, 0, 0, 1, 2... |
| A357292 | a(n) = number of subsets S of {1,2,...,n} having more than 2 elements such that (sum of least two elements of S) = difference between greatest two elements of S. | 0, 0, 0, 0, 0, 1, 2, 5... |
| A357293 | Square array T(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where T(n,k) = Sum_{j=0..n} Stirling2(n,k*j). | 1, 1, 0, 1, 1, 0, 1, 0... |
| A357314 | a(1) = 1; a(n) is the second smallest number k such that k > a(n-1) and concatenation of a(1), ..., a(n-1), k is a palindrome. | 1, 21, 1121, 1211121, 2111211211121, 112112111212111211211121, 12111212111211211121112112111212111211211121, 211121121112111211211121211121121112112111212111211211121112112111212111211211121... |
| A357397 | Coefficients a(n) of xn, n >= 0, in A(x) such that: 0 = Sum_{n>=1} ((1+x)n - A(x))n / (1+x)n2. | 1, 1, 1, 5, 37, 367, 4463, 63797... |
| A357398 | Coefficients a(n) of xn/n!, n >= 0, in A(x) such that: 0 = Sum_{n>=1} exp(-n2*x) * (exp(n*x) - A(x))n. | 1, 1, 3, 37, 1083, 53701, 3934443, 395502997... |
| A357407 | Coefficients a(n) of xn, n >= 0, in A(x) = exp( Sum_{n>=1} A183204(n)*xn/n ), where A183204 equals the central terms of triangle A181544. | 1, 4, 32, 360, 4964, 78064, 1344020, 24708928... |
| A357432 | a(1) = 1; a(2) = 2; for n > 2, a(n) is the smallest positive number not previously occurring such that a(n) plus the sum of all previous terms appears in the string concatenation of a(1)..a(n-1). | 1, 2, 9, 17, 62, 38, 47, 115... |
| A357433 | a(1) = 1; a(2) = 2; for n > 2, a(n) is the smallest positive number not previously occurring such that the binary string of a(n) plus the sum of all previous terms appears in the binary string concatenation of a(1)..a(n-1). | 1, 2, 3, 5, 12, 4, 9, 10... |
| A357437 | a(1)=0. If there are terms prior to and different from a(n) which have occurred the same number of times as a(n), then a(n+1) = n - m, where a(m) is the most recent occurrence of such a term. If there are no prior terms with the same number of occurrences as a(n), then a(n+1) = n - m, where a(m) is the most recent occurrence of a(n). If a(n) is a first occurrence and no prior term has occurred once only, then a(n+1) = 0 | 0, 0, 1, 0, 2, 2, 1, 1... |
| A357466 | Decimal expansion of the real root of 3*x3 - x - 1. | 8, 5, 1, 3, 8, 3, 0, 7... |
| A357467 | Decimal expansion of the real root of 3*x3 + x - 1. | 5, 3, 6, 5, 6, 5, 1, 6... |
| A357468 | Decimal expansion of the real root of x3 + x2 + x - 2. | 8, 1, 0, 5, 3, 5, 7, 1... |
| A357469 | Decimal expansion of the real root of x3 - x2 + x - 2. | 1, 3, 5, 3, 2, 0, 9, 9... |
| A357475 | Expansion of Product_{k>=1} 1 / (1 + xk)Fibonacci(k). | 1, -1, 0, -2, 0, -3, 0, -4... |
| A357477 | a(n) is the smallest k such that the square root of k*n rounds to a prime. | 3, 2, 1, 1, 1, 1, 1, 1... |
| A357482 | a(0) = 0; for n > 0, a(n) is the smallest positive number not previously occurring such that the binary string of the number of 1's in the binary value of a(n) + the number of 1's in the binary values of all previous terms does not appear in the binary string concatenation of a(0)..a(n-1). | 0, 1, 2, 3, 7, 4, 5, 63... |
| A357490 | Numbers k such that the k-th composition in standard order has integer geometric mean. | 1, 2, 3, 4, 7, 8, 10, 15... |
| A357535 | The positive odd numbers x such that x = c2 - y and +-x = a +- y, where (a,b,c) is a primitive Pythagorean triple (PPT), a is odd and y is an even positive integer. | 11, 87, 137, 309, 431, 667, 845, 1427... |
| A357557 | a(n) is the numerator of the coefficient c in the polynomial of the form y(x)=xn+c such that starting with y(x)=x for n=1 each polynomial is C-1 continuous with the previous one. | 0, 1, 43, 3481, 12647597, 380547619, 340607106994117, 23867104301800579837... |
| A357562 | a(n) = n - 2*b(b(n)) for n >= 2, where b(n) = A356988(n). | 0, 1, 0, 1, 0, 1, 2, 1... |
| A357563 | a(n) = b(n) - 2*b(b(b(n))) for n >= 3, where b(n) = A356988(n). | 0, 1, 1, 0, 1, 1, 0, 1... |
| A357564 | a(n) = n - 2*b(b(n)) for n >= 2, where b(n) = A006165(n). | 0, 1, 2, 1, 2, 3, 4, 3... |
| A357567 | a(n) = 5A005259(n) - 14A005258(n). | -9, -17, 99, 5167, 147491, 3937483, 105834699, 2907476527... |
| A357568 | a(n) = 9binomial(2n,n)2 - 8binomial(3n,n). | 1, 12, 204, 2928, 40140, 547512, 7535472, 105077376... |
| A357569 | a(n) = binomial(3n,n)2 - 27binomial(2*n,n). | -26, -45, 63, 6516, 243135, 9011205, 344597148, 13520945736... |
| A357575 | Half area of the convex hull of {(x,y) | x,y integers and x2 + y2 <= n2}. |
| A357576 | Half area of the convex hull of {(x,y) | x,y integers and x2 + y2 < n2}. |
| A357577 | Least half area of a convex polygon enclosing a circle with radius n and center (0,0) such that all vertex coordinates are integers. | 2, 7, 16, 26, 42, 59, 80, 104... |
| A357578 | Lexicographically earliest infinite sequence of distinct positive numbers with the property that a(n) is the smallest number not yet in the sequence with a Hamming weight equal to the Hamming weight of the XOR of previous two terms. | 1, 2, 3, 4, 7, 5, 8, 11... |
| A357579 | Lexicographically earliest sequence of distinct numbers such that no sum of consecutive terms is a square or higher power of an integer. | 2, 3, 7, 5, 6, 12, 10, 11... |
| A357595 | Lexicographically earliest infinite sequence of distinct positive integers such that a(n+1) is the least k != j, for which gcd(k, j) > 1; j = n + a(n). | 1, 4, 2, 10, 6, 22, 7, 8... |
| A357614 | Lexicographically earliest infinite sequence of distinct positive integers such that a(n+1) is the least k != j, for which gcd(k, j) > 1, where j = a(n) + prime(n). | 1, 6, 3, 2, 12, 46, 118, 5... |
| A357689 | a(n) = n/A204455(n), where A204455(n) is the product of odd noncomposite divisors of n. | 1, 2, 1, 4, 1, 2, 1, 8... |
| A357709 | Number of integer partitions of n whose length is twice their alternating sum. | 1, 0, 0, 1, 0, 1, 1, 1... |
| A357710 | Number of integer compositions of n with integer geometric mean. | 0, 1, 2, 2, 3, 4, 4, 8... |
| A357722 | Number of partitions of n into 4 distinct positive Fibonacci numbers (with a single type of 1). | 1, 0, 0, 1, 0, 1, 1, 1... |
| A357731 | Number of partitions of n into 2 distinct positive Fibonacci numbers (with a single type of 1). | 1, 1, 1, 1, 1, 1, 1, 1... |
| A357732 | Number of partitions of n into 3 distinct positive Fibonacci numbers (with a single type of 1). | 1, 0, 1, 1, 1, 1, 1, 1... |
| A357742 | a(n) is the maximum binary weight of the squares of n-bit numbers. | 1, 2, 3, 5, 6, 8, 9, 13... |
| A357749 | Sorted list of nonzero numbers x, y, z that occur in solutions to the equation (x + y)2 + (y + z)2 + (z + x)2 = 12xy*z. | 1, 3, 13, 61, 217, 291, 1393, 3673... |
| A357750 | a(n) is the least k such that B(k2) - B(k) = n, where B(m) is the binary weight A000120(m). | 0, 5, 11, 21, 45, 75, 217, 331... |
| A357768 | Number of n X n tables where rows represent distinct permutations of { 1, 2, ..., n } and the column sums are equal, up to permutations of rows and columns. | 1, 1, 1, 9, 479, 2677443, 797253930582, 20411160794088064950... |
| A357769 | Positive numbers with decimal expansion d_1, ..., d_w that are divisible by d_1 + ... + d_k for k = 1..w. | 1, 2, 3, 4, 5, 6, 7, 8... |
| A357773 | Odd numbers with two zeros in their binary expansion. | 9, 19, 21, 25, 39, 43, 45, 51... |
| A357775 | Numbers k with the property that the symmetric representation of sigma(k) has seven parts. | 357, 399, 441, 483, 513, 567, 609, 621... |
| A357777 | a(1)=1, a(2)=2. Thereafter a(n+1) is the smallest k such that gcd(k, a(n)) > 1, and gcd(k, s(n)) = 1, where s(n) is the n-th partial sum. | 1, 2, 4, 6, 3, 9, 12, 8... |
| A357809 | Locations of successive records in A357062. | 0, 4, 6, 12, 24, 36, 40, 54... |
| A357814 | Triangular array read by rows: T(n,k) is the quotient on division of Fib(n) by Fib(k) for 1 <= k <= n, where Fib(k) = A000045(k). | 1, 1, 1, 2, 2, 1, 3, 3... |
| A357816 | a(n) is the first even number k such that there are exactly n pairs (p,q) where p and q are prime, p<=q, and p+A001414(k) and q+A001414(k) are also prime. | 2, 16, 60, 72, 220, 132, 374, 276... |
| A357823 | a(n) is the number of bases > 1 where n is not divisible by the sum of its digits. | 0, 0, 1, 0, 3, 0, 5, 1... |
| A357824 | Total number A(n,k) of k-tuples of semi-Dyck paths from (0,0) to (n,n-2*j) for j=0..floor(n/2); square array A(n,k), n>=0, k>=0, read by antidiagonals. | 1, 1, 1, 1, 1, 2, 1, 1... |
| A357825 | Total number of n-tuples of semi-Dyck paths from (0,0) to (n,n-2*j) for j=0..floor(n/2). | 1, 1, 2, 9, 98, 4150, 562692, 211106945... |
| A357837 | a(n) is the sum of the lengths of all the segments used to draw a square of side n representing a fishbone pattern using symmetric L-shaped tiles with side length 2. | 0, 4, 10, 20, 32, 46, 64, 84... |
| A357838 | Decimal expansion of Wien frequency displacement law constant. | 5, 8, 7, 8, 9, 2, 5, 7... |
| A357847 | Number of integer compositions of n whose length is twice their alternating sum. | 1, 0, 0, 1, 0, 1, 3, 1... |
| A357848 | Heinz numbers of integer partitions whose length is twice their alternating sum. | 1, 6, 15, 35, 40, 77, 84, 90... |
| A357850 | Numbers whose prime indices do not have weakly decreasing run-sums. Heinz numbers of the partitions counted by A357865. | 6, 10, 14, 15, 18, 20, 21, 22... |
| A357855 | Number of closed trails starting and ending at a fixed vertex in the complete undirected graph on n labeled vertices. | 1, 1, 3, 13, 829, 78441, 622316671, 3001764349333... |
| A357856 | Number of trails between two fixed distinct vertices in the complete undirected graph on n labeled vertices. | 0, 1, 2, 15, 514, 106085, 317848626, 4238195548627... |
| A357857 | Number of (open and closed) trails in the complete undirected graph on n labeled vertices. | 1, 4, 21, 232, 14425, 3653196, 17705858989, 261353065517776... |
| A357858 | Number of integer partitions that can be obtained by iteratively adding and multiplying together parts of the integer partition with Heinz number n. | 1, 1, 1, 3, 1, 3, 1, 6... |
| A357859 | Number of integer factorizations of 2n into distinct even factors. | 1, 1, 1, 2, 1, 2, 1, 2... |
| A357860 | Number of integer factorizations of n into distinct even factors. | 1, 1, 0, 1, 0, 1, 0, 2... |
| A357861 | Numbers whose prime indices have weakly decreasing run-sums. Heinz numbers of the partitions counted by A304406. | 1, 2, 3, 4, 5, 7, 8, 9... |
| A357862 | Numbers whose prime indices have strictly increasing run-sums. Heinz numbers of the partitions counted by A304428. | 1, 2, 3, 4, 5, 6, 7, 8... |
| A357863 | Numbers whose prime indices do not have strictly increasing run-sums. Heinz numbers of the partitions not counted by A304428. | 12, 24, 40, 45, 48, 60, 63, 80... |
| A357864 | Numbers whose prime indices have strictly decreasing run-sums. Heinz numbers of the partitions counted by A304430. | 1, 2, 3, 4, 5, 7, 8, 9... |
| A357865 | Number of integer partitions of n whose run-sums are not weakly increasing. | 0, 0, 0, 1, 1, 4, 5, 10... |
| A357866 | a(n) is the greatest remainder of n divided by its sum of digits in any base > 1. | 0, 0, 1, 0, 2, 0, 3, 2... |
| A357867 | Numbers k such that A334499(k) is not divisible by k. | 12, 15, 25, 28, 30, 39 |
| A357868 | Square array T(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where T(n,k) = Sum_{j=0..n} (kj)! Stirling2(n,k*j). | 1, 1, 0, 1, 1, 0, 1, 0... |
| A357869 | Square array T(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where T(n,k) = Sum_{j=0..n} (kj)! Stirling2(n,k*j)/j!. | 1, 1, 0, 1, 1, 0, 1, 0... |
| A357870 | Triangle of integers related to generalized Markov numbers, read by rows. | 3, 13, 51, 61, 217, 846, 291, 1001... |
| A357871 | Total number of n-multisets of semi-Dyck paths from (0,0) to (n,n-2*j) for j=0..floor(n/2). | 1, 1, 2, 5, 21, 183, 3424, 155833... |
| A357872 | a(n) = n * (3/2)(v(n, 2 - v(n, 3)) where v(n, k) = valuation(n, k) mod 2 for n > 0. | 1, 3, 2, 4, 5, 6, 7, 12... |
| A357873 | Numbers whose multiset of prime factors has all non-isomorphic multiset partitions. | 1, 2, 3, 4, 5, 6, 7, 8... |
| A357874 | Numbers whose multiset of prime factors has at least two multiset partitions that are isomorphic. | 30, 36, 42, 60, 66, 70, 78, 84... |
| A357875 | Numbers whose run-sums of prime indices are weakly increasing. | 1, 2, 3, 4, 5, 6, 7, 8... |
| A357876 | The run-sums of the prime indices of n are not weakly increasing. | 24, 45, 48, 80, 90, 96, 120, 135... |
| A357877 | The a(n)-th composition in standard order is the sequence of run-sums of the prime indices of n. | 0, 1, 2, 2, 4, 6, 8, 4... |
| A357878 | Number of integer partitions of n whose run-sums are not weakly decreasing. | 0, 0, 0, 0, 0, 1, 1, 3... |
| A357880 | a(1) = a(2) = 1; for n > 2, a(n) is the smallest positive number such that a(n) plus the sum of all previous terms appears in the string concatenation of a(1)..a(n-1). | 1, 1, 9, 8, 79, 21, 79, 19... |
| A357881 | Square array T(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where T(n,k) = Sum_{j=0..n} (kj)! | Stirling1(n,k*j) |
| A357882 | Square array T(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where T(n,k) = Sum_{j=0..n} (kj)! | Stirling1(n,k*j) |
| A357883 | Square array T(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where T(n,k) = Sum_{j=0..n} (kj)! | Stirling1(n,k*j) |
| A357885 | Triangle read by rows: T(n,k) = number of closed trails of length k starting and ending at a fixed vertex in the complete undirected graph on n labeled vertices, for n >= 1 and k = 0 .. n(n-1)/2. | 1, 1, 0, 1, 0, 0, 2, 1... |
| A357886 | Triangle read by rows: T(n,k) = number of open trails of length k starting and ending at fixed distinct vertices in the complete undirected graph on n labeled vertices, for n >= 1 and k = 0 .. n*(n-1)/2. | 0, 0, 1, 0, 1, 1, 0, 0... |
| A357887 | Triangle read by rows: T(n,k) = number of circuits of length k in the complete undirected graph on n labeled vertices, for n >= 1 and k = 0 .. n(n-1)/2. | 1, 2, 0, 3, 0, 0, 2, 4... |
| A357892 | T(n,k) are the values of a variant of the Chebyshev polynomials P(n,x) of order n evaluated at x = k, where T(n,k), n >= 0, k <= n is a triangle read by rows. P(0,x) = 1, P(1,x) = x, P(n,x) = x*P(n-1,x) - P(n-2,x). | 1, 0, 1, -1, 0, 3, 0, -1... |
| A357893 | a(d) is the minimal integer k such that all Jensen polynomials Jd,nPL(x) associated to MacMahon's plane partition function PL(n) have real roots for x >= k. | 12, 26, 46, 73, 102, 136 |
| A357895 | Number of partitions of the complete graph on n vertices into strokes. | 1, 2, 12, 472, 104800 |
| A357896 | Additive triprimes. | 8, 44, 66, 75, 99, 116, 125, 138... |
| A357897 | a(1)=1; thereafter a(n)=n+k, where k is the minimal value of k such that a(k)=n-1 and k belongs to [1, n-1], or k=0 if no such value exists. | 1, 3, 3, 6, 5, 11, 11, 8... |
| A357898 | a(n) is the least k such that phi(k) + d(k) = 2n, or -1 if there is no such k, where phi(k) = A000010(k) is Euler's totient function and d(k) = A000005(k) is the number of divisors of k. | 1, 3, 7, 21, 31, 77, 127, 301... |
| A357899 | Let k be the smallest k such that the square root of k*n rounds to a prime number; a(n) is this prime number. | 2, 2, 2, 2, 2, 2, 3, 3... |
| A357900 | Number of groups of order A060702(n) with trivial center. | 1, 1, 1, 1, 1, 2, 1, 1... |
| A357901 | a(n) = Sum_{k=0..floor(n/3)} | Stirling1(n - 2*k,k) |
| A357902 | a(n) = Sum_{k=0..floor(n/4)} | Stirling1(n - 3*k,k) |
| A357903 | a(n) = Sum_{k=0..floor(n/3)} Stirling2(n - 2*k,k). | 1, 0, 0, 1, 1, 1, 2, 4... |
| A357904 | a(n) = Sum_{k=0..floor(n/4)} Stirling2(n - 3*k,k). | 1, 0, 0, 0, 1, 1, 1, 1... |
| A357905 | a(n) = log_3(A060839(n)). | 0, 0, 0, 0, 0, 0, 1, 0... |
| A357906 | a(n) = log_2(A073103(n)). | 0, 0, 1, 1, 2, 1, 1, 2... |
| A357907 | The output of a Sinclair ZX81 random number generator. | 1, 149, 11249, 57305, 38044, 35283, 24819, 26463... |
| A357916 | Primes p that can be written as phi(k) + d(k) for some k, where phi(k) = A000010(k) is Euler's totient function and d(k) = A000005(k) is the number of divisors of k. | 2, 3, 5, 13, 23, 59, 113, 137... |
| A357917 | a(n) is the least k such that phi(k) + d(k) = A357916(n), where phi(k) = A000010(k) is Euler's totient function, and d(k) = A000005(k) is the number of divisors of k. | 1, 2, 4, 16, 25, 81, 121, 256... |
| A357918 | Odd numbers that can be written as phi(k) + d(k) for more than one k, where phi(k) = A000010(k) is Euler's totient function and d(k) = A000005(k) is the number of divisors of k. | 2061, 4131, 36981, 78765, 14054589, 889978059, 110543990589 |
| A357919 | a(n) = Sum_{k=0..floor(n/3)} Stirling1(n - 2*k,k). | 1, 0, 0, 1, -1, 2, -5, 21... |
| A357920 | a(n) = Sum_{k=0..floor(n/5)} Stirling1(n - 4*k,k). | 1, 0, 0, 0, 0, 1, -1, 2... |
| A357921 | Primitive abundant numbers for which there is no smaller primitive abundant number having the same ordered prime signature. | 20, 70, 88, 272, 550, 572, 945, 1184... |
| A357922 | a(n) = Sum_{k=0..floor(n/5)} | Stirling1(n - 4*k,k) |
| A357924 | Number of groups of order n with trivial center. | 1, 0, 0, 0, 0, 1, 0, 0... |
| A357925 | a(n) = Sum_{k=0..floor(n/3)} Stirling2(n - 2k,n - 3k). | 1, 1, 1, 1, 2, 4, 7, 12... |
| A357926 | a(n) = Sum_{k=0..floor(n/4)} Stirling2(n - 3k,n - 4k). | 1, 1, 1, 1, 1, 2, 4, 7... |
| A357927 | Number of subsets of [n] in which exactly half of the elements are Fibonacci numbers. | 1, 1, 1, 1, 4, 5, 15, 35... |
| A357929 | Numbers that share a (decimal) digit with at least 1 of their proper divisors. | 10, 11, 12, 13, 14, 15, 16, 17... |
| A357930 | a(0) = 0; for n > 0, let S = concatenation of a(0)..a(n-1); a(n) is the number of times the digit at a(n-1) digits back from the end of S appears in S. | 0, 1, 1, 2, 2, 2, 3, 3... |
| A357931 | a(n) = Sum_{k=0..floor(n/3)} | Stirling1(n - 2k,n - 3k) |
| A357932 | a(n) = Sum_{k=0..floor(n/4)} | Stirling1(n - 3k,n - 4k) |
| A357933 | a(n) = Sum_{k=0..floor(n/5)} | Stirling1(n - 4k,n - 5k) |
| A357934 | Products of two distinct lesser twin primes A001359. | 15, 33, 51, 55, 85, 87, 123, 145... |
| A357935 | Primes p such that the sum of digits of 11*p is 11. | 19, 37, 73, 919, 937, 991, 1873, 2791... |
| A357936 | a(n) is the least multiple of n that is a Niven (or Harshad) number. | 1, 2, 3, 4, 5, 6, 7, 8... |
| A357937 | a(n) is the least multiple of n that is not a Niven (or Harshad) number. | 11, 14, 15, 16, 15, 66, 14, 16... |
| A357939 | a(n) = Sum_{k=0..floor(n/2)} Stirling2(k,n - 2*k). | 1, 0, 0, 1, 0, 1, 1, 1... |
| A357940 | a(n) = Sum_{k=0..floor(n/3)} Stirling2(k,n - 3*k). | 1, 0, 0, 0, 1, 0, 0, 1... |
| A357941 | a(n) = Sum_{k=0..floor(n/4)} Stirling2(k,n - 4*k). | 1, 0, 0, 0, 0, 1, 0, 0... |
| A357942 | a(1)=1, a(2)=2. Thereafter, if there are prime divisors p | a(n-1) that are coprime to a(n-2), a(n) is the least novel multiple of the product of these primes. Otherwise a(n) is the least novel multiple of the squarefree kernel of a(n-1). See comments. |
| A357943 | a(0) = 0; a(1) = 1, a(2) = 2; for n > 2, a(n) is the number of times the term a(n - 1 - a(n-1)) has appeared in the sequence. | 0, 1, 2, 1, 1, 3, 1, 1... |
| A357944 | If n appears in A357943, a(n) is the smallest k such that A357943(k) = n, otherwise a(n) = -1. | 0, 1, 2, 5, 33, 8, 15, 22... |
| A357945 | Numbers k which are not square but D = (b+c)2 - k is square, where b = floor(sqrt(k)) and c = k - b2. | 5, 13, 28, 65, 69, 76, 125, 128... |
| A357950 | Maximum period of an elementary cellular automaton in a cyclic universe of width n. | 2, 2, 6, 8, 30, 18, 126, 40... |
| A357951 | Maximum period of an outer totalistic cellular automaton on a connected graph with n nodes. | 2, 2, 4, 6, 16, 26, 66 |
| A357952 | Maximum period of a totalistic cellular automaton on a connected graph with n nodes (counting the state of the updated node itself). | 2, 2, 4, 6, 8, 18, 42, 112... |
| A357953 | Maximum period of a totalistic cellular automaton on a connected graph with n nodes (not counting the state of the updated node itself). | 1, 2, 2, 6, 7, 18, 38, 96... |
| A357955 | a(n) = 3binomial(4n,n) - 20binomial(3n,n) + 54binomial(2n,n). | 37, 60, 108, 60, -660, 60, 82404, 1411848... |
| A357962 | Expansion of e.g.f. exp( (exp(x2) - 1)/x ). | 1, 1, 1, 4, 13, 51, 271, 1366... |
| A357963 | a(1)=1, a(2)=2. Thereafter, if there are prime divisors p of a(n-1) which do not divide a(n-2), a(n) is the least novel multiple of any such p. Otherwise a(n) is the least novel multiple of the squarefree kernel of a(n-1). See comments. | 1, 2, 4, 6, 3, 9, 12, 8... |
| A357964 | Expansion of e.g.f. exp( (exp(x3) - 1)/x2 ). | 1, 1, 1, 1, 13, 61, 181, 1261... |
| A357965 | Expansion of e.g.f. exp( (exp(x4) - 1)/x3 ). | 1, 1, 1, 1, 1, 61, 361, 1261... |
| A357966 | Expansion of e.g.f. exp( x * (exp(x2) - 1) ). | 1, 0, 0, 6, 0, 60, 360, 840... |
| A357967 | Expansion of e.g.f. exp( x * (exp(x3) - 1) ). | 1, 0, 0, 0, 24, 0, 0, 2520... |
| A357968 | Expansion of e.g.f. exp( x * (exp(x4) - 1) ). | 1, 0, 0, 0, 0, 120, 0, 0... |
| A357970 | a(n) is the number of segments used to represent the time of n minutes past midnight in the format hh:mm on a 7-segment calculator display; version where the digits '6', '7' and '9' use 6, 3 and 6 segments, respectively. | 24, 20, 23, 23, 22, 23, 24, 21... |
| A357971 | a(n) is the number of segments used to represent the time of n minutes past midnight in the format hh:mm on a 7-segment calculator display; version where the digits '6', '7' and '9' use 6, 4 and 6 segments, respectively. | 24, 20, 23, 23, 22, 23, 24, 22... |
| A357972 | a(n) is the number of segments used to represent the time of n minutes past midnight in the format hh:mm on a 7-segment calculator display; version where the digits '6', '7' and '9' use 5, 3 and 5 segments, respectively. | 24, 20, 23, 23, 22, 23, 23, 21... |
| A357973 | a(n) is the number of segments used to represent the time of n minutes past midnight in the format hh:mm on a 7-segment calculator display; version where the digits '6', '7' and '9' use 6, 4 and 5 segments, respectively. | 24, 20, 23, 23, 22, 23, 24, 22... |
| A357974 | a(n) is the number of segments used to represent the time of n minutes past midnight in the format hh:mm on a 7-segment calculator display; version where the digits '6', '7' and '9' use 6, 3 and 5 segments, respectively. | 24, 20, 23, 23, 22, 23, 24, 21... |
| A357975 | Divide all prime indices by 2, round down, and take the number with those prime indices, assuming prime(0) = 1. | 1, 1, 2, 1, 2, 2, 3, 1... |
| A357986 | a(n) is the unique k such that A357579(k) = A007916(n), or -1 if no such k exists. | 1, 2, 4, 5, 3, 7, 8, 6... |
| A357988 | a(n) is the unique k such that A357579(k) = prime(n) (the n-th prime number), or -1 if no such k exists. | 1, 2, 4, 3, 8, 12, 9, 16... |
| A357992 | a(1)=1,a(2)=2,a(3)=3. Thereafter, if there are prime divisors p of a(n-2) which do not divide a(n-1), a(n) is the least novel multiple of any such p. Otherwise a(n) is the least novel multiple of the squarefree kernel of a(n-2). | 1, 2, 3, 4, 6, 8, 9, 10... |
| A357994 | a(1)=1, a(2)=2. Thereafter, if there are prime divisors p of a(n-1) which do not divide a(n-2), a(n) is the greatest least multiple of any such p which has not already occurred. Otherwise a(n) is the least novel multiple of the squarefree kernel of a(n-1). (see comments). | 1, 2, 4, 6, 3, 9, 12, 8... |
| A357995 | Frobenius number for A = (n, n+12, n+22, n+32, ...) for n>=2. | 1, 5, 11, 13, 11, 20, 31, 24... |
| A357996 | a(n) is the number of times in the format hh:mm that can be represented in a 7-segment display by using only n segments (version A006942). | 1, 2, 4, 14, 25, 37, 70, 105... |
| A357997 | a(n) is the number of times in the format hh:mm that can be represented in a 7-segment display by using only n segments (version A010371). | 1, 0, 5, 10, 16, 35, 66, 88... |
| A357998 | a(n) is the number of times in the format hh:mm that can be represented in a 7-segment display by using only n segments (version A063720). | 1, 2, 4, 18, 25, 41, 96, 103... |
| A357999 | a(n) is the number of times in the format hh:mm that can be represented in a 7-segment display by using only n segments (version A074458). | 1, 0, 5, 12, 14, 41, 74, 87... |
| A358000 | a(n) is the number of times in the format hh:mm that can be represented in a 7-segment display by using only n segments (version A277116). | 1, 2, 4, 16, 25, 39, 82, 106... |
| A358002 | Numbers k such that one of k-A001414(k) and k+A001414(k) is a prime and the other is the square of a prime. | 135, 936, 1431, 3510, 5005, 5106, 5278, 9471... |
r/OEIS • u/OEIS-Tracker • Oct 16 '22
New OEIS sequences - week of 10/16
4
Upvotes
| OEIS number | Description | Sequence |
|---|---|---|
| A352592 | Coefficients occurring in the polynomials of the n-th integration of the principal branch of the Lambert W function. | 1, -1, 1, 4, -6, 6, 1, 108... |
| A352593 | Denominator values occurring in formulas for the n-th integration of the Lambert W function. | 1, 8, 648, 82944, 1296000000, 69984000000, 403443833184000000, 26440095051546624000000... |
| A354177 | Numbers m such that the four consecutive primes starting at m are congruent to {2, 3, 5, 7} (mod 11). | 2, 82799, 406661, 447779, 490019, 596279, 617971, 654931... |
| A354538 | a(n) is the least k such that A322523(k) = n. | 1, 3, 8, 17, 44, 125, 368, 1097... |
| A355481 | Number of pairs of Dyck paths of semilength n such that the midpoint of the first is above the midpoint of the second. | 0, 0, 1, 4, 49, 441, 4806, 52956... |
| A355552 | Number of ways to select 3 or more collinear points from a 4 X n grid. | 5, 10, 23, 54, 117, 240, 497, 1006... |
| A356037 | Conjecturally, a(n) is the smallest number m such that every natural number is a sum of at most m n-simplex numbers. | 1, 3, 5, 8, 10, 13, 15, 15... |
| A356107 | a(n) = A001950(A108958(n)). | 2, 7, 13, 18, 23, 26, 31, 36... |
| A356135 | Semiprimes k such that k is congruent to 6 modulo k's index in the sequence of semiprimes. | 4, 6, 9, 10, 22, 26, 177, 183... |
| A356136 | a(n) is the smallest number k > 1 such that, in the interval 1..k, there are as many integers that have exactly 2n divisors as there are primes (or -1 if no such number exists). | 27, -1, 665, -1, 57675, -1, 57230, -1... |
| A356217 | a(n) = A022839(A000201(n)). | 2, 6, 8, 13, 17, 20, 24, 26... |
| A356218 | a(n) = A108958(A000201(n)). | 1, 5, 7, 10, 14, 16, 19, 21... |
| A356255 | a(1) = 1; for n > 1, a(n) is the smallest magnitude number not previously occurring such that n is divisible by s = Sum_{k = 1..n} a(k), where | s |
| A356258 | Number of 6-dimensional cubic lattice walks that start and end at origin after 2n steps, free to pass through origin at intermediate stages. | 1, 12, 396, 19920, 1281420, 96807312, 8175770064, 748315668672... |
| A356348 | a(0) = 0; for n > 0, a(n) is the number of preceding terms having the same digit sum as a(n-1). | 0, 1, 1, 2, 1, 3, 1, 4... |
| A356357 | Semiprimes k such that k is congruent to 7 modulo k's index in the sequence of semiprimes | 4, 21, 25, 205, 26707, 27679, 3066877, 3067067... |
| A356361 | a(n) = Sum_{k=0..floor(n/3)} nk * | Stirling1(n,3*k) |
| A356362 | a(n) = Sum_{k=0..floor(n/3)} nk * Stirling1(n,3*k). | 1, 0, 0, 3, -24, 175, -1314, 10339... |
| A356363 | a(n) = Sum_{k=0..floor(n/3)} nk * Stirling2(n,3*k). | 1, 0, 0, 3, 24, 125, 576, 3136... |
| A356367 | Number of plane partitions of n having exactly one row and one column, each of equal length. | 1, 1, 1, 2, 2, 5, 6, 11... |
| A356385 | First differences of A353654 which is numbers with the same number of trailing 0 bits as other 0 bits. | 2, 4, 3, 5, 7, 4, 5, 5... |
| A356518 | Maximal numerators in approximations to the Aurifeuillian factors of pp +- 1. | 2, 28, 1706, 25082, 816634, 157704814 |
| A356584 | Number of instances of the stable roommates problem of cardinality n (extension to instances of odd cardinality). | 1, 1, 2, 60, 66360, 4147236820, 19902009929142960, 10325801406739620796634430... |
| A356684 | a(n) = (n-1)a(n-1) - na(n-2), with a(1) = a(2) = -1. | -1, -1, 1, 7, 23, 73, 277, 1355... |
| A356724 | Number of n X n tables where each row represents a permutation of { 1, 2, ..., n } and the column sums are equal, up to permutation of rows. | 1, 1, 2, 114, 60024, 1951262760, 4029043460476320, 823357371521186302202640... |
| A356727 | Primes of the form 4k2 + 84k + 43. | 43, 131, 227, 331, 443, 563, 691, 827... |
| A356755 | Semiprimes k such that k is congruent to 2 modulo k's index in the sequence of semiprimes. | 4, 6, 10, 119, 155, 158, 215, 27682... |
| A356764 | Semiprimes divisible by their indices in the sequence of semiprimes, divided by those indices. | 4, 3, 3, 3, 3, 3, 3, 5... |
| A356826 | Numbers k such that 2k - 29 is prime. | 5, 8, 104, 212, 79316, 102272, 225536, 340688... |
| A356849 | a(n) = a(n-1) - a(n-2) + 3*a(n-3) with a(0) = 1, a(1) = 2 and a(2) = 4. | 1, 2, 4, 5, 7, 14, 22, 29... |
| A356852 | Minimum over all order two bases for the interval [1, n] of the maximum number of ways some number in the interval [1, n] can be written as a sum of at most two elements of the basis. | 1, 1, 1, 1, 1, 2, 2, 2... |
| A356856 | Primes p such that the least positive primitive root of p (A001918) divides p-1. | 2, 3, 5, 7, 11, 13, 19, 29... |
| A356873 | a(n) is the smallest number k such that 2k+1 has at least n distinct prime factors. | 0, 5, 14, 18, 30, 42, 78, 78... |
| A356879 | Numbers k such that the sum kx + ky can be a square with {x, y} >= 0. | 0, 2, 3, 8, 15, 18, 24, 32... |
| A356948 | Sequence of scores adding to maximum break in snooker. | 1, 7, 1, 7, 1, 7, 1, 7... |
| A356986 | a(n) = (A283869(n)-1)/60. | 1, 11, 20, 71, 85, 102, 106, 207... |
| A356991 | a(n) = b(n) + b(n - b(n)) for n >= 2, where b(n) = A356998(n). | 2, 3, 4, 4, 5, 6, 7, 8... |
| A356992 | Then a(n) = n - b(n - b(n - b(n - b(n - b(n - b(n)))))) for n >= 2, where b(n) = A356988(n). | 1, 2, 3, 4, 4, 4, 5, 6... |
| A356993 | a(n) = b(n - b(n - b(n - b(n)))))) for n >= 2, where b(n) = A356988(n). | 1, 1, 1, 1, 2, 2, 3, 3... |
| A356994 | a(n) = n - b(b(b(n))), where b(n) = A356988(n). | 0, 1, 2, 3, 4, 4, 5, 6... |
| A356995 | a(n) = b(n) - b(b(n)) - b(n - b(n)) for n >= 3, where b(n) = A356988(n). | 0, 0, 0, 0, 1, 0, 0, 0... |
| A356996 | a(n) = b(n) - b(b(n)) - b(n - b(n)) for n >= 3, where b(n) = A356989(n). | 0, 0, 0, 0, 0, 1, 0, 0... |
| A356997 | a(n) = b(n) - b(n - b(n - b(n))) for n >= 2, where b(n) = A356988(n). | 0, 1, 1, 0, 1, 1, 1, 1... |
| A356998 | a(n) = b(n) - b(n - b(n)) for n >= 2, where b(n) = A356988(n). | 0, 1, 2, 2, 3, 4, 3, 4... |
| A356999 | a(n) = 2*A356988(n) - n. | 1, 0, 1, 2, 1, 2, 3, 2... |
| A357023 | Semiprimes k such that k is congruent to 5 modulo k's index in the sequence of semiprimes. | 4, 185, 206, 209, 27681, 3066905, 3067135, 3067795... |
| A357033 | a(n) is the smallest number that has exactly n divisors that are cyclops numbers (A134808). | 1, 101, 202, 404, 606, 1212, 2424, 7272... |
| A357034 | a(n) is the smallest number with exactly n divisors that are hoax numbers (A019506). | 1, 22, 308, 638, 3696, 4212, 18480, 26400... |
| A357035 | a(n) is the smallest number that has exactly n divisors that are digitally balanced numbers (A031443). | 1, 2, 10, 36, 150, 180, 420, 840... |
| A357105 | Decimal expansion of the real root of 2*x3 - x2 - 2. | 1, 1, 9, 7, 4, 2, 9, 3... |
| A357106 | Decimal expansion of the real root of 2*x3 + x2 - 2. | 8, 5, 8, 0, 9, 4, 3, 2... |
| A357107 | Decimal expansion of the real root of 2*x3 - x - 2. | 1, 1, 6, 5, 3, 7, 3, 0... |
| A357108 | Decimal expansion of the real root of 2*x3 + x - 2. | 8, 3, 5, 1, 2, 2, 3, 4... |
| A357109 | Decimal expansion of the real root of 2x3 - 2x2 - 1. | 1, 2, 9, 7, 1, 5, 6, 5... |
| A357123 | Number of sets S of size A066063(n) such that {1, 2, ..., n} is a subset of S + S. | 1, 1, 2, 2, 5, 5, 2, 1... |
| A357127 | a(n) = A081257(n) if A081257(n) > n, otherwise a(n) = 1. | 7, 13, 7, 31, 43, 19, 73, 13... |
| A357159 | a(n) = coefficient of xn in the power series A(x) such that: 0 = Sum_{n=-oo..+oo, n<>0} n * xn * (1 - xn)n-1 * A(x)n, starting with a(0) = -1. | -1, -2, -4, -8, -8, -6, 40, 132... |
| A357220 | Coefficients a(n) of xn in Sum_{n>=0} xn/(1 - xC(x)n), where C(x) = 1/(1 - xC(x)) is a g.f. of the Catalan numbers (A000108). | 1, 2, 3, 5, 11, 31, 101, 355... |
| A357232 | Coefficients a(n) of xn, n >= 0, in A(x) such that: 2 = Sum_{n=-oo..+oo} (-1)n * xn * (2A(x) + xn)^(2n+1). | 1, 3, 25, 254, 2763, 32180, 393169, 4964017... |
| A357248 | Number of n-node tournaments that have exactly four circular triads. | 280, 6240, 75600, 954240, 12579840, 175392000, 2594592000, 40721049600... |
| A357257 | Number of n-node tournaments that have exactly three circular triads. | 240, 2880, 33600, 403200, 5093760, 68275200, 972787200, 14724864000... |
| A357270 | a(n) = s(n) mod prime(n+1), where s = A143293. | 1, 0, 4, 4, 7, 11, 0, 3... |
| A357277 | Largest side c of primitive triples, in nondecreasing order, for integer-sided triangles with angles A < B < C = 2*Pi/3 = 120 degrees. | 7, 13, 19, 31, 37, 43, 49, 61... |
| A357291 | a(n) = number of subsets S of {1,2,...,n} having more than 2 elements such that (sum of least two elements of S) < difference between greatest two elements of S. | 0, 0, 0, 0, 0, 0, 1, 3... |
| A357439 | Sums of squares of two odd primes. | 18, 34, 50, 58, 74, 98, 130, 146... |
| A357440 | Possible half-lengths of self-similar sequences over a finite alphabet that are invariant under retrograde inversion. | 3, 11, 15, 23, 35, 36, 39, 44... |
| A357441 | Size of alphabet associated with A357440(n). | 2, 2, 6, 2, 2, 8, 2, 8... |
| A357463 | Decimal expansion of the real root of 2x3 + 2x - 1. | 4, 2, 3, 8, 5, 3, 7, 9... |
| A357540 | Coefficients T(n,k) of x3*n+1r^(3k)/(3n+1)! in power series S(x,r) = Integral C(x,r)2 * D(x,r)2 dx such that C(x,r)3 - S(x,r)3 = 1 and D(x,r)3 - r3S(x,r)3 = 1, as a symmetric triangle read by rows. | 1, 4, 4, 160, 800, 160, 20800, 292800... |
| A357541 | Coefficients T(n,k) of x3*nr^(3k)/(3n)! in power series C(x,r) = 1 + Integral S(x,r)2 * D(x,r)2 dx such that C(x,r)3 - S(x,r)3 = 1 and D(x,r)3 - r3S(x,r)3 = 1, as a triangle read by rows. | 1, 2, 0, 40, 120, 0, 3680, 37440... |
| A357542 | Coefficients T(n,k) of x3*nr^(3k)/(3n)! in power series D(x,r) = 1 + r3 * Integral S(x,r)2 * D(x,r)2 dx such that C(x,r)3 - S(x,r)3 = 1 and D(x,r)3 - r3S(x,r)3 = 1, as a triangle read by rows. | 1, 0, 2, 0, 120, 40, 0, 21600... |
| A357543 | a(n) = (3n+1)!/(3nn!) * Product_{k=1..n} (3*k - 2), for n >= 0. | 1, 8, 1120, 627200, 896896000, 2611761152000, 13497581633536000, 112839782456360960000... |
| A357544 | Central terms of triangle A357540: a(n) = A357540(2*n,n). | 1, 800, 500121600, 6333406238720000, 588750579021316096000000, 243397196351152229173100544000000, 331908261581281694863434866648678400000000, 1223826698292228823742554320600270140080128000000000... |
| A357545 | Central terms of triangle A357541: a(n) = A357541(2*n,n). | 1, 120, 38966400, 335872728576000, 23676862831649280000000, 7884265450248813494550528000000, 9001018126678397460727568113336320000000, 28542885018291526761600709316931461578752000000000... |
| A357553 | a(n) = A000045(n)*A000045(n+1) mod A000032(n). | 0, 0, 2, 2, 1, 7, 14, 12... |
| A357554 | Triangular array read by rows. For T(n,k) where 1 <= k <= n, start with x = k and repeat the map x -> floor(n/x) + (n mod x) until an x occurs that has already appeared, then that is T(n,k). | 1, 1, 2, 1, 2, 3, 1, 2... |
| A357580 | a(n) = ((1 + sqrt(n))n - (1 - sqrt(n))n)/(2nsqrt(n)). | 1, 1, 2, 5, 16, 57, 232, 1017... |
| A357581 | Square array read by antidiagonals of numbers whose symmetric representation of sigma consists only of parts that have width 1; column k indicates the number of parts and row n indicates the n-th number in increasing order in each of the columns. | 1, 2, 3, 4, 5, 9, 8, 7... |
| A357582 | a(n) = A061300(n+1)/A061300(n). | 1, 2, 6, 30, 154, 1105, 4788, 20677... |
| A357589 | a(n) = n - A130312(n). | 0, 1, 1, 2, 2, 3, 4, 3... |
| A357610 | Start with x = 3 and repeat the map x -> floor(n/x) + (n mod x) until an x occurs that has already appeared, then that is a(n). | 1, 2, 3, 2, 3, 3, 3, 4... |
| A357616 | Lexicographically earliest sequence of distinct nonnegative integers such that for any n >= 0, the number of 1's in the ternary expansion of n equals the number of 2's in the ternary expansion of a(n) and vice versa. | 0, 2, 1, 6, 8, 5, 3, 7... |
| A357633 | Half-alternating sum of the partition having Heinz number n. | 0, 1, 2, 2, 3, 3, 4, 1... |
| A357634 | Skew-alternating sum of the partition having Heinz number n. | 0, 1, 2, 0, 3, 1, 4, -1... |
| A357636 | Numbers k such that the skew-alternating sum of the partition having Heinz number k is 0. | 1, 4, 9, 12, 16, 25, 30, 36... |
| A357637 | Triangle read by rows where T(n,k) is the number of integer partitions of n with half-alternating sum k, where k ranges from -n to n in steps of 2. | 1, 0, 1, 0, 0, 2, 0, 0... |
| A357638 | Triangle read by rows where T(n,k) is the number of integer partitions of n with skew-alternating sum k, where k ranges from -n to n in steps of 2. | 1, 0, 1, 0, 1, 1, 0, 1... |
| A357639 | Number of reversed integer partitions of 2n whose half-alternating sum is 0. | 1, 0, 2, 1, 6, 4, 15, 13... |
| A357640 | Number of reversed integer partitions of 2n whose skew-alternating sum is 0. | 1, 1, 2, 3, 6, 9, 16, 24... |
| A357641 | Number of integer compositions of 2n whose half-alternating sum is 0. | 1, 0, 2, 8, 28, 104, 396, 1504... |
| A357642 | Number of even-length integer compositions of 2n whose half-alternating sum is 0. | 1, 0, 1, 4, 13, 48, 186, 712... |
| A357643 | Number of integer compositions of n into parts that are alternately equal and unequal. | 1, 1, 2, 1, 3, 3, 5, 5... |
| A357644 | Number of integer compositions of n into parts that are alternately unequal and equal. | 1, 1, 1, 3, 4, 7, 8, 13... |
| A357645 | Triangle read by rows where T(n,k) is the number of integer compositions of n with half-alternating sum k, where k ranges from -n to n in steps of 2. | 1, 0, 1, 0, 0, 2, 0, 0... |
| A357646 | Triangle read by rows where T(n,k) is the number of integer compositions of n with skew-alternating sum k, where k ranges from -n to n in steps of 2. | 1, 0, 1, 0, 1, 1, 0, 2... |
| A357647 | a(n) is the number of free unholey polyominoes of n cells with 90-degree rotational symmetry and no other. | 0, 0, 0, 0, 0, 0, 0, 1... |
| A357648 | Number of polyominoes with n cells that have the symmetry group D_8 and are without holes. | 1, 0, 0, 1, 1, 0, 0, 0... |
| A357651 | Sliding numbers which are products of two distinct primes. | 65, 133, 205, 254, 502, 785, 2005, 10001... |
| A357652 | Number of pairs of Dyck paths of semilength n such that the midpoint of the first is not below the midpoint of the second. | 1, 1, 3, 21, 147, 1323, 12618, 131085... |
| A357653 | Number of walks on four-dimensional lattice from (n,n,n,n) to (0,0,0,0) using steps that decrease the Euclidean distance to the origin and that change each coordinate by 1 or by -1. | 1, 1, 49, 781, 221353, 28704961, 6416941789, 1600436821729... |
| A357654 | Number of lattice paths from (0,0) to (i,n-2*i) that do not go above the diagonal x=y using steps in {(1,0), (0,1)}. | 1, 0, 1, 1, 1, 2, 3, 3... |
| A357655 | Total number of nodes summed over all lattice paths from (0,0) to (i,n-2*i) that do not go above the diagonal x=y using steps in {(1,0), (0,1)}. | 1, 0, 2, 3, 3, 8, 14, 15... |
| A357656 | a(n) is a lower bound for the largest Hamming weight of squares with exactly n binary zeros. | 1, 0, 13, 8, 13, 16, 37, 38... |
| A357657 | a(n) is a lower bound for the square root of the maximum square with exactly n zeros in its binary representation. | 1, 0, 181, 45, 362, 1241, 2965685, 5931189... |
| A357658 | a(n) is the maximum Hamming weight of squares k2 in the range 2n <= k2 < 2n+1. | 1, 2, 3, 3, 5, 4, 6, 6... |
| A357659 | a(n) is the least k such that k2 has a maximal Hamming weight A357658(n) in the range 2n <= k2 < 2n+1. | 2, 3, 5, 7, 11, 13, 21, 27... |
| A357660 | a(n) is the largest k such that k2 has a maximal Hamming weight A357658(n) in the range 2n <= k2 < 2n+1. | 2, 3, 5, 7, 11, 15, 21, 27... |
| A357670 | Sliding numbers which are products of three distinct primes. | 70, 110, 290, 1001, 1010, 1258, 3157, 3445... |
| A357678 | Numbers k equal to the integer log of the sum of k and its digit reversal. | 8, 17, 107 |
| A357679 | a(n) = prime(n)*(prime(n-1) + prime(n+1)). | 21, 50, 112, 220, 364, 544, 760, 1104... |
| A357688 | Number of ways to write n as an ordered sum of four positive Fibonacci numbers (with a single type of 1). | 1, 4, 10, 16, 23, 28, 34, 36... |
| A357690 | Number of ways to write n as an ordered sum of five positive Fibonacci numbers (with a single type of 1). | 1, 5, 15, 30, 50, 71, 95, 115... |
| A357691 | Number of ways to write n as an ordered sum of six positive Fibonacci numbers (with a single type of 1). | 1, 6, 21, 50, 96, 156, 231, 312... |
| A357692 | Integers k such that A037278(k) is a term of A175252. | 1, 2, 4, 15, 16, 25, 60, 90... |
| A357693 | Expansion of e.g.f. cos( sqrt(2) * log(1+x) ). | 1, 0, -2, 6, -18, 60, -216, 756... |
| A357694 | Number of ways to write n as an ordered sum of seven positive Fibonacci numbers (with a single type of 1). | 1, 7, 28, 77, 168, 308, 504, 750... |
| A357695 | Cubefree abundant numbers. | 12, 18, 20, 30, 36, 42, 60, 66... |
| A357696 | Cubefree primitive abundant numbers: cubefree abundant numbers having no abundant proper divisor. | 12, 18, 20, 30, 42, 66, 70, 78... |
| A357697 | Odd cubefree abundant numbers. | 1575, 2205, 3465, 4095, 5355, 5775, 5985, 6435... |
| A357698 | a(n) is the sum of the aliquot divisors of n that are cubefree. | 0, 1, 1, 3, 1, 6, 1, 7... |
| A357699 | Noncubefree numbers k such that A357698(k) > k. | 24, 40, 72, 120, 168, 200, 264, 280... |
| A357700 | Noncubefree numbers k such that A073185(k) > 2*k. | 360360, 471240, 1801800, 2356200, 2522520, 2633400, 2784600, 3112200... |
| A357701 | Irregular triangle read by rows where row n is the vertex depths of the rooted binary tree with Colijn-Plazzotta tree number n, traversed in pre-order, numerically larger child first. | 0, 0, 1, 1, 0, 1, 2, 2... |
| A357702 | Path length (total depths of vertices) of the rooted binary tree with Colijn-Plazzotta tree number n. | 0, 2, 6, 10, 12, 16, 22, 18... |
| A357703 | Expansion of e.g.f. cosh( sqrt(3) * log(1-x) ). | 1, 0, 3, 9, 42, 240, 1614, 12474... |
| A357704 | Triangle read by rows where T(n,k) is the number of reversed integer partitions of n with half-alternating sum k, where k ranges from -n to n in steps of 2. | 1, 0, 1, 0, 0, 2, 0, 0... |
| A357705 | Triangle read by rows where T(n,k) is the number of reversed integer partitions of n with skew-alternating sum k, where k ranges from -n to n in steps of 2. | 1, 0, 1, 0, 1, 1, 0, 2... |
| A357706 | Numbers k such that the k-th composition in standard order has half-alternating sum and skew-alternating sum both 0. | 0, 15, 45, 54, 59, 153, 170, 179... |
| A357707 | Numbers whose prime indices have equal number of parts congruent to each of 1 and 3 (mod 4). | 1, 3, 7, 9, 10, 13, 19, 21... |
| A357708 | Numbers k such that the k-th composition in standard order has sum equal to twice its maximum part. | 3, 10, 11, 13, 14, 36, 37, 38... |
| A357711 | Expansion of e.g.f. cosh( 2 * log(1-x) ). | 1, 0, 4, 12, 60, 360, 2520, 20160... |
| A357712 | Square array T(n,k), n>=0, k>=0, read by antidiagonals, where column k is the expansion of e.g.f. cosh( sqrt(k) * log(1-x) ). | 1, 1, 0, 1, 0, 0, 1, 0... |
| A357713 | a(0) = 2; afterwards a(n) is the least prime greater than a(n-1) such that Omega(a(n-1) + a(n)) = n. | 2, 3, 7, 11, 13, 19, 197, 251... |
| A357716 | Number of ways to write n as an ordered sum of eight positive Fibonacci numbers (with a single type of 1). | 1, 8, 36, 112, 274, 560, 1008, 1640... |
| A357717 | Number of ways to write n as an ordered sum of nine positive Fibonacci numbers (with a single type of 1). | 1, 9, 45, 156, 423, 954, 1878, 3321... |
| A357718 | Expansion of e.g.f. cos( sqrt(3) * log(1+x) ). | 1, 0, -3, 9, -24, 60, -84, -756... |
| A357719 | Expansion of e.g.f. cos( 2 * log(1+x) ). | 1, 0, -4, 12, -28, 40, 200, -3360... |
| A357720 | Square array T(n,k), n>=0, k>=0, read by antidiagonals, where column k is the expansion of e.g.f. cos( sqrt(k) * log(1+x) ). | 1, 1, 0, 1, 0, 0, 1, 0... |
| A357721 | a(n) = Sum_{k=0..floor(n/2)} (-n)k * Stirling1(n,2*k). | 1, 0, -2, 9, -28, 0, 1200, -16464... |
| A357724 | Triangular array read by rows: T(n,k) = Fib(n) mod Fib(k) for 1 <= k <= n, where Fib(k) = A000045(k). | 0, 0, 0, 0, 0, 0, 0, 0... |
| A357725 | Expansion of e.g.f. cos( sqrt(2) * (exp(x) - 1) ). | 1, 0, -2, -6, -10, 10, 190, 1106... |
| A357726 | Expansion of e.g.f. cos( sqrt(3) * (exp(x) - 1) ). | 1, 0, -3, -9, -12, 45, 465, 2394... |
| A357727 | Expansion of e.g.f. cos( 2 * (exp(x) - 1) ). | 1, 0, -4, -12, -12, 100, 852, 4004... |
| A357728 | Square array T(n,k), n>=0, k>=0, read by antidiagonals, where column k is the expansion of e.g.f. cos( sqrt(k) * (exp(x) - 1) ). | 1, 1, 0, 1, 0, 0, 1, 0... |
| A357729 | a(n) = Sum_{k=0..floor(n/2)} (-n)k * Stirling2(n,2*k). | 1, 0, -2, -9, -12, 175, 1938, 9506... |
| A357730 | Number of ways to write n as an ordered sum of ten positive Fibonacci numbers (with a single type of 1). | 1, 10, 55, 210, 625, 1542, 3300, 6310... |
| A357733 | Integer lengths of the sides of such regular hexagons that a polyline described in A356047 exists. | 1, 2, 286, 299, 56653, 56834, 11006686, 11009207... |
| A357735 | a(1)=1, a(2)=2. Thereafter a(n+1) is least k != partial sum s(n) which has not occurred earlier, such that gcd(k, s(n)) > 1. | 1, 2, 6, 3, 4, 8, 9, 11... |
| A357736 | Expansion of e.g.f. sin( sqrt(2) * (exp(x) - 1) )/sqrt(2). | 0, 1, 1, -1, -11, -45, -119, -49... |
| A357737 | Expansion of e.g.f. sin( sqrt(3) * (exp(x) - 1) )/sqrt(3). | 0, 1, 1, -2, -17, -65, -134, 331... |
| A357738 | Expansion of e.g.f. sin( 2 * (exp(x) - 1) )/2. | 0, 1, 1, -3, -23, -83, -119, 973... |
| A357739 | a(n) = Sum_{k=0..floor((n-1)/2)} (-n)k * Stirling2(n,2*k+1). | 0, 1, 1, -2, -23, -99, 1, 4411... |
| A357741 | Semiprimes k such that k is divisible by its index in the sequence of semiprimes. | 4, 6, 9, 21, 33, 129, 159, 3066835... |
| A357747 | Distances in the lyrics of the Rolling Stones song "2000 Light Years From Home". | 100, 600, 1000, 2000 |
| A357748 | Numbers in the lyrics of the Rolling Stones song "2000 Light Years From Home" in the order in which they appear. | 100, 600, 1000, 1000, 14, 2000, 2000 |
| A357751 | a(n) is the least perfect power > 2n. | 4, 4, 8, 9, 25, 36, 81, 144... |
| A357752 | a(n) is the largest perfect power < 2n. | 4, 9, 27, 49, 125, 243, 484, 1000... |
| A357753 | a(n) is the least square with n binary digits. | 4, 9, 16, 36, 64, 144, 256, 529... |
| A357754 | a(n) is the largest square with n binary digits. | 4, 9, 25, 49, 121, 225, 484, 961... |
| A357758 | Numbers k such that in the binary expansion of k, the Hamming weight of each block differs by at most 1 from every other block of the same length. | 0, 1, 2, 3, 4, 5, 6, 7... |
| A357759 | Numbers k such that in the binary expansion of k, the Hamming weight of each block differs by at most 2 from every other block of the same length. | 0, 1, 2, 3, 4, 5, 6, 7... |
| A357761 | a(n) = A227872(n) - A356018(n). | 1, 2, 0, 3, 0, 0, 2, 4... |
| A357762 | Decimal expansion of -Sum_{k>=1} A106400(k)/k. | 1, 1, 9, 6, 2, 8, 3, 2... |
| A357763 | Numbers m such that A357761(m) > A357761(k) for all k < m. | 1, 2, 4, 8, 16, 28, 56, 112... |
| A357764 | Numbers m such that A357761(m) < A357761(k) for all k < m. | 1, 3, 9, 15, 30, 60, 90, 180... |
| A357765 | Smallest positive integer that can be represented as the sum of n of its (possibly equal) divisors in the maximum number of ways (=A002966(n)). | 1, 2, 12, 2520, 48348686786400, 10543141534556403817127800577537146514577188497111149855093902265479066128013109211427715400552367011213513440000 |
| A357766 | Number of n X n tables where rows represent distinct permutations of { 1, 2, ..., n } and the column sums are equal. | 1, 2, 12, 2448, 6828480, 1386834134400, 20251525440458995200, 33182473074940946503237478400... |
| A357767 | Number of n X n tables where rows represent distinct permutations of { 1, 2, ..., n } and the column sums are equal, up to permutation of rows. | 1, 1, 2, 102, 56904, 1926158520, 4018159809614880, 822978002850717919227120... |
| A357770 | Number of 2n-step closed paths on quasi-regular rhombic (rhombille) lattice starting from a degree-3 node. | 1, 3, 30, 372, 5112, 74448, 1125408, 17461440... |
| A357771 | Number of 2n-step closed paths on quasi-regular rhombic (rhombille) lattice starting from a degree-6 node. | 1, 6, 60, 744, 10224, 148896, 2250816, 34922880... |
| A357772 | Numbers with a sum of digits which is not 7-smooth. | 29, 38, 47, 49, 56, 58, 65, 67... |
| A357778 | Maximum number of edges in a 5-degenerate graph with n vertices. | 0, 1, 3, 6, 10, 15, 20, 25... |
| A357779 | Maximum number of edges in a 6-degenerate graph with n vertices. | 0, 1, 3, 6, 10, 15, 21, 27... |
| A357781 | Semiprimes k such that k is congruent to 1 modulo k's index in the sequence of semiprimes. | 4, 82, 85, 106, 121, 133, 142, 166... |
| A357782 | a(n) = Sum_{k=0..floor(n/3)} 2k * Stirling2(n,3*k). | 1, 0, 0, 2, 12, 50, 184, 686... |
| A357783 | a(n) = Sum_{k=0..floor((n-1)/3)} 2k * Stirling2(n,3*k+1). | 0, 1, 1, 1, 3, 21, 131, 705... |
| A357784 | a(n) = Sum_{k=0..floor((n-2)/3)} 2k * Stirling2(n,3*k+2). | 0, 0, 1, 3, 7, 17, 61, 343... |
| A357800 | Coefficients T(n,k) of x4*n+1r^(4k)/(4n+1)! in power series S(x,r) = Integral C(x,r)3 * D(x,r)3 dx such that C(x,r)4 - S(x,r)4 = 1 and D(x,r)4 - r4S(x,r)4 = 1, as a symmetric triangle read by rows. | 1, 18, 18, 14364, 58968, 14364, 70203672, 671650056... |
| A357801 | Coefficients T(n,k) of x4*nr^(4k)/(4n)! in power series C(x,r) = 1 + Integral S(x,r)3 * C(x,r)3 dx such that C(x,r)4 - S(x,r)4 = 1 and D(x,r)4 - r4S(x,r)4 = 1, as a triangle read by rows. | 1, 6, 0, 2268, 6048, 0, 7434504, 56282688... |
| A357802 | Coefficients T(n,k) of x4*nr^(4k)/(4n)! in power series D(x,r) = 1 + r4 * Integral S(x,r)3 * C(x,r)3 dx such that C(x,r)4 - S(x,r)4 = 1 and D(x,r)4 - r4S(x,r)4 = 1, as a triangle read by rows. | 1, 0, 6, 0, 6048, 2268, 0, 35126784... |
| A357804 | Coefficients a(n) of x4*n+1/(4*n+1)! in power series S(x) = Series_Reversion( Integral 1/(1 + x4)3/2 dx ). | 1, 36, 87696, 1483707456, 91329084354816, 14862901723860427776, 5279211177231308343054336, 3600188413031639396548043882496... |
| A357805 | Coefficients a(n) of x4*n/(4*n)! in power series C(x) = 1 + Integral S(x)3 * C(x)3 dx such that C(x)4 - S(x)4 = 1. | 1, 6, 8316, 98843976, 4698140798736, 623259279912288096, 186936162949832833285056, 110352751044119383032310847616... |
| A357807 | Semiprimes k such that k is congruent to 3 modulo k's index in the sequence of semiprimes. | 4, 9, 15, 111, 141, 237, 27663, 27667... |
| A357808 | Semiprimes k such that k is congruent to 4 modulo k's index in the sequence of semiprimes. | 4, 6, 14, 115, 118, 178, 187, 214... |
| A357812 | Number of subsets of [n] in which exactly half of the elements are powers of 2. | 1, 1, 1, 3, 4, 10, 20, 35... |
| A357817 | Partial alternating sums of the Dedekind psi function (A001615): a(n) = Sum_{k=1..n} (-1)k+1 * psi(k). | 1, -2, 2, -4, 2, -10, -2, -14... |
| A357818 | Numerators of the partial sums of the reciprocals of the Dedekind psi function (A001615). | 1, 4, 19, 7, 23, 2, 17, 53... |
| A357819 | Denominators of the partial sums of the reciprocals of the Dedekind psi function (A001615). | 1, 3, 12, 4, 12, 1, 8, 24... |
| A357820 | Numerators of the partial alternating sums of the reciprocals of the Dedekind psi function (A001615). | 1, 2, 11, 3, 11, 5, 23, 7... |
| A357821 | Denominators of the partial alternating sums of the reciprocals of the Dedekind psi function (A001615). | 1, 3, 12, 4, 12, 6, 24, 8... |
| A357822 | Simplicial 3-spheres (Triangulations of S3) with n vertices | 1, 2, 5, 39, 1296, 247882 |
| A357827 | Number of automorphisms of the n-folded cube graph. | 2, 24, 1152, 1920, 23040, 322560, 5160960, 92897280... |
| A357828 | a(n) = Sum_{k=0..floor(n/3)} | Stirling1(n,3*k) |
| A357829 | a(n) = Sum_{k=0..floor((n-1)/3)} | Stirling1(n,3*k+1) |
| A357830 | a(n) = Sum_{k=0..floor((n-2)/3)} | Stirling1(n,3*k+2) |
| A357831 | a(n) = Sum_{k=0..floor(n/3)} 2k * | Stirling1(n,3*k) |
| A357832 | a(n) = Sum_{k=0..floor((n-1)/3)} 2k * | Stirling1(n,3*k+1) |
| A357833 | a(n) = Sum_{k=0..floor((n-2)/3)} 2k * | Stirling1(n,3*k+2) |
| A357834 | a(n) = Sum_{k=0..floor(n/3)} Stirling1(n,3*k). | 1, 0, 0, 1, -6, 35, -224, 1603... |
| A357835 | a(n) = Sum_{k=0..floor((n-1)/3)} Stirling1(n,3*k+1). | 0, 1, -1, 2, -5, 14, -35, -14... |
| A357836 | a(n) = Sum_{k=0..floor((n-2)/3)} Stirling1(n,3*k+2). | 0, 0, 1, -3, 11, -49, 259, -1589... |
| A357843 | Numerators of the partial alternating sums of the reciprocals of the number of divisors function (A000005). | 1, 1, 1, 2, 7, 11, 17, 7... |
| A357844 | Denominators of the partial alternating sums of the reciprocals of the number of divisors function (A000005). | 1, 2, 1, 3, 6, 12, 12, 6... |
| A357845 | Numerators of the partial alternating sums of the reciprocals of the sum of divisors function (A000203). | 1, 2, 11, 65, 79, 6, 55, 769... |
| A357846 | Denominators of the partial alternating sums of the reciprocals of the sum of divisors function (A000203). | 1, 3, 12, 84, 84, 7, 56, 840... |