A260793 Primes p such that p does not divide any term of the Apéry-like sequence A000172 (also known as Type I primes).

3, 11, 17, 19, 43, 83, 89, 97, 113, 137, 139, 163, 193, 211, 233, 241, 283, 307, 313, 331, 347, 353, 379, 401, 409, 419, 433, 443, 491, 499, 523, 547, 569, 587, 601, 617, 619, 641, 643, 673, 811, 827, 859, 881, 929, 947, 953, 977, 1009, 1019, 1033, 1049, 1051

Offset: 1

Author

N. J. A. Sloane, Aug 05 2015

Keywords

• nonn

Comments

See Schulte et al. (2014) for the precise definition of Type I primes.

Links

• Amita Malik and Armin Straub, Divisibility properties of sporadic Apéry-like numbers, Research in Number Theory, 2016, 2:5
• 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
• A. Schulte, S. VanSchalkwyk, A. Yang, On the divisibility and valuations of the Franel numbers, in MSRI-UP Research Reports, 2014.
• A. Schulte, S. VanSchalkwyk, A. Yang, On the divisibility and valuations of the Franel numbers, Examples of Outstanding Student Posters, MAA.

Crossrefs

Cf. A260791, A260792.

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.

Programs

Mathematica

maxPrime = 1051;
maxPi = PrimePi @ maxPrime;
okQ[p_] := AllTrue[Range[3 maxPi (* coeff 3 is empirical *)], GCD[HypergeometricPFQ[{-#, -#, -#}, {1, 1}, -1], p] == 1&];
Select[Prime[Range[maxPi]], okQ] (* Jean-François Alcover, Jan 13 2020 *)

Extensions

Edited by N. J. A. Sloane, Aug 22 2017