OFFSET
1,1
COMMENTS
Malik and Straub give arguments suggesting that this sequence is infinite. - N. J. A. Sloane, Aug 06 2017
LINKS
Robert Price, Table of n, a(n) for n = 1..758
Amita Malik and Armin Straub, Divisibility properties of sporadic Apéry-like numbers, Research in Number Theory, 2016, 2:5.
Amita Malik, List of all primes up to 10000 in this sequence and in A260793, A291275-A291284, together with Mathematica code.
E. Rowland, R. Yassawi, Automatic congruences for diagonals of rational functions, arXiv preprint arXiv:1310.8635 [math.NT], 2013.
MATHEMATICA
NeverDividesLucasSeqQ[a_, p_] := And @@ Table[Mod[a[n], p]>0, {n, 0, p-1}];
A3[a_, b_, c_, n_ /; n < 0] = 0;
A3[a_, b_, c_, 0] = 1;
A3[a_, b_, c_, n_] := A3[a, b, c, n] = (((2n - 1)(a (n-1)^2 + a (n-1) + b)) A3[a, b, c, n-1] - c (n-1)^3 A3[a, b, c, n-2])/n^3;
A3[a_, b_, c_, d_, n_ /; n < 0] = 0;
Agamma[n_] := A3[17, 5, 1, n];
Select[Range[1000], PrimeQ[#] && NeverDividesLucasSeqQ[Agamma, #]&] (* Jean-François Alcover, Aug 05 2018, copied from Amita Malik's notebook *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Philippe Deléham, Oct 27 2007
EXTENSIONS
Terms a(16) onwards computed by Amita Malik - N. J. A. Sloane, Aug 21 2017
STATUS
approved