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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. 4
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 2 05:15 EDT 2022. Contains 357191 sequences. (Running on oeis4.)