A291275 Primes p such that p does not divide any term of the Apéry-like sequence A005258.

2, 5, 13, 17, 29, 37, 41, 61, 73, 89, 101, 109, 137, 149, 173, 181, 197, 229, 233, 269, 277, 313, 337, 349, 353, 373, 397, 401, 409, 433, 457, 461, 541, 557, 601, 613, 641, 661, 673, 677, 701, 709, 733, 761, 769, 797, 821, 829, 853, 857, 877, 929, 941, 977

Offset

1,1

Links

Table of n, a(n) for n=1..54.

Amita Malik and Armin Straub, Mathematica notebook for generating A133370 and A260793, A291275-A291284

Amita Malik and Armin Straub, Lists of all primes up to 10000 in A133370 and A260793, A291275-A291284, together with Mathematica code.

Amita Malik and Armin Straub, Divisibility properties of sporadic Apéry-like numbers, Research in Number Theory, 2016, 2:5.

Mathematica

maxPrime = 977;
maxPi = PrimePi @ maxPrime;
okQ[p_] := AllTrue[Range[3 maxPi (* coeff 3 is empirical *)], GCD[HypergeometricPFQ[{# + 1, -#, -#}, {1, 1}, 1], p] == 1&];
Select[Prime[Range[maxPi]], okQ] (* Jean-François Alcover, Jan 13 2020 *)

Crossrefs

For primes that do not divide the terms of the sequences A000172, A005258, A002893, A081085, A006077, A093388, A125143, A229111, A002895, A290575, A290576, A005259 see A260793, A291275-A291284 and A133370 respectively.

Sequence in context: A002313 A233346 A182198 * A291278 A177349 A160215

Adjacent sequences: A291272 A291273 A291274 * A291276 A291277 A291278

Keyword

nonn

Author

N. J. A. Sloane, Aug 21 2017

Status

approved