A135845 Prime numbers p not of the form 10k+1 for which the quintic polynomial x^5-x-1 modulus p is factorizable into five binomials.

1973, 3769, 7727, 11903, 14629, 16903, 17737, 18097, 19477, 20747, 20759, 21727, 22717, 23567, 25037, 27397, 27529, 28279, 29207, 29959, 30497, 31319, 33289, 36097, 37463, 42139, 42487, 42689, 45959, 46229, 47309, 47969, 48847, 48947

Offset

1,1

Comments

This sequence is a subsequence of A135844.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Maple

filter:= proc(p) isprime(p) and nops([msolve(x^5-x-1, p)])=5 end proc:
select(filter, [seq(seq(10*k+j, j=[3, 7, 9]), k=0..10000)]); # Robert Israel, Jul 03 2018

Mathematica

a = {}; Do[If[Mod[Prime[n], 1, poly = PolynomialMod[x^5 - 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, A135846, A135847.

Sequence in context: A251816 A108386 A135844 * A121995 A061998 A205653

Adjacent sequences: A135842 A135843 A135844 * A135846 A135847 A135848

Keyword

nonn

Author

Artur Jasinski, Dec 01 2007

Status

approved