A057485 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).

10, 12, 15, 18, 25, 31, 34, 52, 55, 57, 127, 172, 220, 300, 393, 492, 772, 807, 972, 1023, 1266, 1564, 2220, 2242, 3585, 5314, 7306, 8719, 10777, 23647, 26119, 33127, 48036, 48945, 59172, 68841, 131071, 214780, 236892, 265857, 341841, 563599, 841444, 901057

Offset

1,1

Comments

Any subsequent terms are > 10^6. - Lucas A. Brown, Dec 07 2022

Links

Table of n, a(n) for n=1..44.

Prog

(PARI) isok(n) = polisirreducible(Mod(1, 2)*x^n+(x^8-1)/(x-1)); \\ Michel Marcus, Apr 15 2020
(SageMath) P.<x> = GF(2)[]
from itertools import count
for n in count(8):
    print('\b'*42, n, end='', flush=True)
    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

Crossrefs

Sequence in context: A248715 A054518 A072198 * A162825 A107836 A096128

Adjacent sequences: A057482 A057483 A057484 * A057486 A057487 A057488

Keyword

nonn,hard

Author

Robert G. Wilson v, Sep 27 2000

Extensions

a(17)-a(25) from Jinyuan Wang, Apr 15 2020

a(26)-a(44) from Lucas A. Brown, Dec 07 2022

Status

approved