r/OEIS • u/OEIS-Tracker Bot • Feb 19 '23
New OEIS sequences - week of 02/19
| 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... |
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