A057485 - OEIS

%I #21 Dec 08 2022 07:29:56

%S 10,12,15,18,25,31,34,52,55,57,127,172,220,300,393,492,772,807,972,

%T 1023,1266,1564,2220,2242,3585,5314,7306,8719,10777,23647,26119,33127,

%U 48036,48945,59172,68841,131071,214780,236892,265857,341841,563599,841444,901057

%N Numbers k>7 such that x^k + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1 is irreducible over GF(2).

%C Any subsequent terms are > 10^6. - _Lucas A. Brown_, Dec 07 2022

%o (PARI) isok(n) = polisirreducible(Mod(1,2)*x^n+(x^8-1)/(x-1)); \\ _Michel Marcus_, Apr 15 2020

%o (SageMath) P.<x> = GF(2)[]

%o from itertools import count

%o for n in count(8):

%o     print('\b'*42, n, end='', flush=True)

%o     if (x^n + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1).is_irreducible(): print() # _Lucas A. Brown_, Dec 07 2022

%K nonn,hard

%O 1,1

%A _Robert G. Wilson v_, Sep 27 2000

%E a(17)-a(25) from _Jinyuan Wang_, Apr 15 2020

%E a(26)-a(44) from _Lucas A. Brown_, Dec 07 2022