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%I #6 May 09 2021 10:51:04
%S 599,733,3163,4259,4397,5419,6637,6733,8009,9803,14923,20627,20873,
%T 22777,26339,27947,29339,29389,29527,29917,34123,34739,34757,36527,
%U 36809,38783,40433,42859,43049,43963,45763,51659,52223,52747,54917
%N Prime numbers p not of the form 10k+1 for which the quintonacci quintic polynomial x^5 - x^4 - x^3 - x^2 - x - 1 modulus p is factorizable into five binomials.
%C This sequence is a subsequence of A135846.
%t a = {}; Do[If[Mod[Prime[n], 10] 1, poly = PolynomialMod[x^5-x^4-x^3-x^2-x-1, Prime[n]]; c = FactorList[poly, Modulus -> Prime[n]]; If[Sum[c[[m]][[2]], {m, 1, Length[c]}] == 6, AppendTo[a, Prime[n]]]], {n, 1, 10000}]; a
%Y Cf. A135842, A135843, A135844, A135845, A135847.
%K nonn
%O 1,1
%A _Artur Jasinski_, Dec 01 2007
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