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A135846 Prime numbers p for which quintonacci quintic polynomial x^5-x^4-x^3-x^2-x-1 modulus p is completely factorizable. 3
599, 691, 733, 3163, 4259, 4397, 5419, 6637, 6733, 8009, 8311, 9803, 11731, 14923, 17291, 20627, 20873, 22777, 25111, 26339, 27947, 29339, 29389, 29527, 29917, 34123, 34421, 34739, 34757, 36527, 36809, 38783, 40433, 40531, 41131, 42859 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

A135847 and A135843 are complementary subsets of this sequence.

LINKS

Table of n, a(n) for n=1..36.

MATHEMATICA

a = {}; Do[If[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: A029562 A273810 A095746 * A035209 A135847 A106762

Adjacent sequences:  A135843 A135844 A135845 * A135847 A135848 A135849

KEYWORD

nonn

AUTHOR

Artur Jasinski, Dec 01 2007

STATUS

approved

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Last modified May 16 15:15 EDT 2022. Contains 353706 sequences. (Running on oeis4.)