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

1,1

Comments

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

Links

Table of n, a(n) for n=1..53.

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.

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 *)

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.

Sequence in context: A309581 A291277 A191375 * A057179 A322962 A075334

Adjacent sequences: A260790 A260791 A260792 * A260794 A260795 A260796

Keyword

nonn

Author

N. J. A. Sloane, Aug 05 2015

Extensions

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

Status

approved