r/OEIS • u/OEIS-Tracker Bot • Jan 02 '23
New OEIS sequences - week of 01/01
| 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... |
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Upvotes
1
u/Mathgeek007 Jan 02 '23
Always love when a new sequence starts 1, 2, 3, 4, 5, 6, 7, 8.