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

Author

Joerg Arndt, Mar 02 2016

Keywords

• nonn
• more
• hard

Comments

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

Crossrefs

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

Programs

PARI

isok(n) = polisirreducible(Mod(1, 2)*x^n * (x+1)^(n-1) + 1); \\ Michel Marcus, Mar 03 2016

Sage

P. = GF(2)[]
for n in range(1, 10^5):
       if (x^n * (x+1)^(n-1) + 1).is_irreducible():
           print(n)

Extensions

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