

A133370


Primes p such that p does not divide any term of the Apery sequence A005259 .


24



2, 3, 7, 13, 23, 29, 43, 47, 53, 67, 71, 79, 83, 89, 101, 103, 107, 109, 113, 127, 131, 137, 149, 157, 167, 173, 199, 223, 229, 239, 263, 269, 277, 281, 311, 313, 317, 337, 349, 353, 359, 373, 383, 389, 397, 401, 409, 421, 449, 457, 461, 467, 479, 487, 491
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OFFSET

1,1


COMMENTS

Malik and Straub give arguments suggesting that this sequence is infinite.  N. J. A. Sloane, Aug 06 2017


LINKS

Robert Price, Table of n, a(n) for n = 1..758
Amita Malik and Armin Straub, Divisibility properties of sporadic Apérylike numbers, Research in Number Theory, 2016, 2:5.
Amita Malik, Mathematica notebook for generating this sequence and A260793, A291275A291284
Amita Malik, List of all primes up to 10000 in this sequence and in A260793, A291275A291284, together with Mathematica code.
E. Rowland, R. Yassawi, Automatic congruences for diagonals of rational functions, arXiv preprint arXiv:1310.8635 [math.NT], 2013.


MATHEMATICA

NeverDividesLucasSeqQ[a_, p_] := And @@ Table[Mod[a[n], p]>0, {n, 0, p1}];
A3[a_, b_, c_, n_ /; n < 0] = 0;
A3[a_, b_, c_, 0] = 1;
A3[a_, b_, c_, n_] := A3[a, b, c, n] = (((2n  1)(a (n1)^2 + a (n1) + b)) A3[a, b, c, n1]  c (n1)^3 A3[a, b, c, n2])/n^3;
A3[a_, b_, c_, d_, n_ /; n < 0] = 0;
Agamma[n_] := A3[17, 5, 1, n];
Select[Range[1000], PrimeQ[#] && NeverDividesLucasSeqQ[Agamma, #]&] (* JeanFrançois Alcover, Aug 05 2018, copied from Amita Malik's notebook *)


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, A291275A291284 and A133370 respectively.
Sequence in context: A003509 A238432 A238423 * A237283 A182047 A291544
Adjacent sequences: A133367 A133368 A133369 * A133371 A133372 A133373


KEYWORD

nonn


AUTHOR

Philippe Deléham, Oct 27 2007


EXTENSIONS

Terms a(16) onwards computed by Amita Malik  N. J. A. Sloane, Aug 21 2017


STATUS

approved



