A057489 Numbers n > 13 such that x^n + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1 is irreducible over GF(2).

15, 21, 25, 42, 43, 48, 60, 97, 106, 133, 147, 148, 178, 201, 252, 253, 327, 513, 570, 732, 763, 1108, 1342, 1572, 2175, 2407, 2605, 2850, 3930, 4627, 6181, 6312, 7048, 7596, 8995, 9250, 9873, 11841, 12471, 13927, 20658, 20965, 33957, 72373, 91992, 156657

Offset

1,1

Comments

No terms == 2 mod 3 or == 4 mod 5. - Robert Israel, Feb 22 2017

Links

Table of n, a(n) for n=1..46.

Maple

Q:= add(x^i, i=0..13):
select(t -> Irreduc(x^t+Q) mod 2, [$14..1000]); # Robert Israel, Feb 22 2017

Prog

(PARI) isok(n) = (n>13) && polisirreducible(Mod(1, 2)*(x^n+sum(k=0, 13, x^k))); \\ Michel Marcus, Feb 23 2017

Crossrefs

Sequence in context: A129926 A020204 A280389 * A070811 A211375 A326387

Adjacent sequences: A057486 A057487 A057488 * A057490 A057491 A057492

Keyword

nonn

Author

Robert G. Wilson v, Sep 28 2000

Extensions

a(22)-a(24) from Robert Israel, Feb 22 2017

a(25)-a(32) from Jinyuan Wang, Apr 15 2020

a(33)-a(47) from Lucas A. Brown, Nov 29 2022

Status

approved