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A135845 Prime numbers p not of the form 10k+1 for which quintic polynomial x^5-x-1 modulus p is factorizable into five binomials. 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

This sequence is a subset 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

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Last modified August 18 15:00 EDT 2019. Contains 326106 sequences. (Running on oeis4.)