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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). 0
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Any subsequent terms are > 10^6. - Lucas A. Brown, Dec 05 2022
LINKS
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
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

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Last modified July 25 02:50 EDT 2024. Contains 374585 sequences. (Running on oeis4.)