A268274 Numbers n such that x^n * (x+1)^(n-1) + 1 is irreducible over GF(2).

1, 2, 3, 4, 5, 8, 21, 32, 33, 36, 53, 64, 85, 89, 148, 312, 404, 3080, 8380, 11684, 16384, 18089, 21096, 53492, 78484, 192248

Offset

1,2

Comments

Any subsequent terms are > 2 * 10^5. - Lucas A. Brown, Dec 01 2022

Links

Table of n, a(n) for n=1..26.

Prog

(Sage)
P.<x> = GF(2)[]
for n in range(1, 10^5):
       if (x^n * (x+1)^(n-1) + 1).is_irreducible():
           print(n)
(PARI) isok(n) = polisirreducible(Mod(1, 2)*x^n * (x+1)^(n-1) + 1); \\ Michel Marcus, Mar 03 2016

Crossrefs

Cf. A162570 (corresponding to powers of 2 in this sequence).

Sequence in context: A057657 A293591 A116657 * A079383 A103670 A289081

Adjacent sequences: A268271 A268272 A268273 * A268275 A268276 A268277

Keyword

nonn,more,hard

Author

Joerg Arndt, Mar 02 2016

Extensions

a(26) from Lucas A. Brown, Dec 01 2022

Status

approved