A135847 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.

599, 733, 3163, 4259, 4397, 5419, 6637, 6733, 8009, 9803, 14923, 20627, 20873, 22777, 26339, 27947, 29339, 29389, 29527, 29917, 34123, 34739, 34757, 36527, 36809, 38783, 40433, 42859, 43049, 43963, 45763, 51659, 52223, 52747, 54917

Offset

1,1

Comments

This sequence is a subsequence of A135846.

Links

Table of n, a(n) for n=1..35.

Mathematica

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

Crossrefs

Cf. A135842, A135843, A135844, A135845, A135847.

Sequence in context: A135846 A035209 A356531 * A106762 A158277 A250937

Adjacent sequences: A135844 A135845 A135846 * A135848 A135849 A135850

Keyword

nonn

Author

Artur Jasinski, Dec 01 2007

Status

approved