A057487 Numbers n > 9 such that x^n + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x +1 is irreducible over GF(2).

10, 14, 20, 50, 52, 64, 104, 119, 155, 167, 170, 205, 386, 464, 617, 3005, 3962, 4033, 4199, 4445, 4648, 4706, 6835, 8473, 14755, 20233, 23890, 73654, 88097, 110050, 123292, 252220, 254624, 363167, 399220, 475744, 532639, 608300, 778490, 912836, 924889

Offset

1,1

Comments

Any subsequent terms are > 10^6. - Lucas A. Brown, Dec 05 2022

Links

Table of n, a(n) for n=1..41.

Prog

(PARI) isok(n) = n>9 && polisirreducible(Mod(1, 2)*x^n+(x^10-1)/(x-1)); \\ Michel Marcus, Apr 15 2020
(SageMath) P.<x> = GF(2)[]
from itertools import count
for n in count(10):
    print('\b'*42, n, end='', flush=True)
    if (x^n + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1).is_irreducible(): print() # Lucas A. Brown, Dec 05 2022

Crossrefs

Sequence in context: A246473 A063920 A269703 * A073486 A073487 A325161

Adjacent sequences: A057484 A057485 A057486 * A057488 A057489 A057490

Keyword

nonn,hard

Author

Robert G. Wilson v, Sep 28 2000

Extensions

a(16)-a(22) from Jinyuan Wang, Apr 15 2020

a(23)-a(41) from Lucas A. Brown, Dec 05 2022

Status

approved