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A260793
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Primes p such that p does not divide any term of the Apéry-like sequence A000172 (also known as Type I primes).
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26
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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
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OFFSET
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1,1
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COMMENTS
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See Schulte et al. (2014) for the precise definition of Type I primes.
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LINKS
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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.
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MATHEMATICA
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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 *)
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CROSSREFS
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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
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane, Aug 05 2015
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EXTENSIONS
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Edited by N. J. A. Sloane, Aug 22 2017
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STATUS
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approved
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