A135846 Prime numbers p for which quintonacci quintic polynomial x^5-x^4-x^3-x^2-x-1 modulus p is completely factorizable.

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

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 A356531 A135847

Adjacent sequences: A135843 A135844 A135845 * A135847 A135848 A135849

Keyword

nonn

Author

Artur Jasinski, Dec 01 2007

Status

approved