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%I #13 Jan 13 2020 09:35:03
%S 2,5,13,17,29,37,41,61,73,89,101,109,137,149,173,181,197,229,233,269,
%T 277,313,337,349,353,373,397,401,409,433,457,461,541,557,601,613,641,
%U 661,673,677,701,709,733,761,769,797,821,829,853,857,877,929,941,977
%N Primes p such that p does not divide any term of the Apéry-like sequence A005258.
%H Amita Malik and Armin Straub, <a href="/A133370/a133370.nb">Mathematica notebook for generating A133370 and A260793, A291275-A291284</a>
%H Amita Malik and Armin Straub, <a href="/A133370/a133370.pdf">Lists of all primes up to 10000 in A133370 and A260793, A291275-A291284, together with Mathematica code.</a>
%H Amita Malik and Armin Straub, <a href="https://doi.org/10.1007/s40993-016-0036-8">Divisibility properties of sporadic Apéry-like numbers</a>, Research in Number Theory, 2016, 2:5.
%t maxPrime = 977;
%t maxPi = PrimePi @ maxPrime;
%t okQ[p_] := AllTrue[Range[3 maxPi (* coeff 3 is empirical *)], GCD[HypergeometricPFQ[{# + 1, -#, -#}, {1, 1}, 1], p] == 1&];
%t Select[Prime[Range[maxPi]], okQ] (* _Jean-François Alcover_, Jan 13 2020 *)
%Y 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.
%K nonn
%O 1,1
%A _N. J. A. Sloane_, Aug 21 2017
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