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 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. 4

%I

%S 1973,3769,7727,11903,14629,16903,17737,18097,19477,20747,20759,21727,

%T 22717,23567,25037,27397,27529,28279,29207,29959,30497,31319,33289,

%U 36097,37463,42139,42487,42689,45959,46229,47309,47969,48847,48947

%N 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.

%C This sequence is a subsequence of A135844.

%H Robert Israel, <a href="/A135845/b135845.txt">Table of n, a(n) for n = 1..10000</a>

%p filter:= proc(p) isprime(p) and nops([msolve(x^5-x-1,p)])=5 end proc:

%p select(filter, [seq(seq(10*k+j,j=[3,7,9]),k=0..10000)]); # _Robert Israel_, Jul 03 2018

%t 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]][], {m, 1, Length[c]}] == 6, AppendTo[a, Prime[n]]]], {n, 1, 10000}]; a

%Y Cf. A135842, A135843, A135844, A135846, A135847.

%K nonn

%O 1,1

%A _Artur Jasinski_, Dec 01 2007

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Last modified September 29 09:23 EDT 2022. Contains 357088 sequences. (Running on oeis4.)