Nothing Special   »   [go: up one dir, main page]

login
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).
0
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
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 A376372 A107836
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