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%I #26 Jan 13 2020 09:34:56
%S 3,11,17,19,43,83,89,97,113,137,139,163,193,211,233,241,283,307,313,
%T 331,347,353,379,401,409,419,433,443,491,499,523,547,569,587,601,617,
%U 619,641,643,673,811,827,859,881,929,947,953,977,1009,1019,1033,1049,1051
%N Primes p such that p does not divide any term of the Apéry-like sequence A000172 (also known as Type I primes).
%C See Schulte et al. (2014) for the precise definition of Type I primes.
%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
%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
%H A. Schulte, S. VanSchalkwyk, A. Yang, <a href="http://www.msri.org/system/cms/files/81/files/original/Research_Reports_2014_MSRI-UP_(Single_File).pdf#page=130">On the divisibility and valuations of the Franel numbers</a>, in MSRI-UP Research Reports, 2014.
%H A. Schulte, S. VanSchalkwyk, A. Yang, <a href="http://www.maa.org/sites/default/files/doc/images/VanSchalkwykAlgebra.pdf">On the divisibility and valuations of the Franel numbers</a>, Examples of Outstanding Student Posters, MAA.
%t maxPrime = 1051;
%t maxPi = PrimePi @ maxPrime;
%t okQ[p_] := AllTrue[Range[3 maxPi (* coeff 3 is empirical *)], GCD[HypergeometricPFQ[{-#, -#, -#}, {1, 1}, -1], p] == 1&];
%t Select[Prime[Range[maxPi]], okQ] (* _Jean-François Alcover_, Jan 13 2020 *)
%Y Cf. A260791, A260792.
%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 this sequence, A291275-A291284 and A133370 respectively.
%K nonn
%O 1,1
%A _N. J. A. Sloane_, Aug 05 2015
%E Edited by _N. J. A. Sloane_, Aug 22 2017
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