A058334 Numbers n such that the trinomial x^n + x + 1 is irreducible over GF(5).

0, 1, 2, 3, 7, 18, 22, 27, 31, 78, 94, 115, 171, 402, 438, 507, 1363, 1467, 2263, 2283, 3627, 9247, 9955

Offset: 1

Author

Robert G. Wilson v, Dec 13 2000

Keywords

• nonn
• more

Comments

No other n < 4400. - Michael Somos, Mar 12 2007

Next term > 10^4. [Joerg Arndt, Mar 02 2016]

Crossrefs

Cf. A002475 (GF(2)), A058857 (GF(7)).

Programs

PARI

isok(n) = polisirreducible(Mod(1, 5)*(x^n + x + 1)); \\ Michel Marcus, Feb 11 2014

Sage

P. = GF(5)[]
for n in range(0, 10000):
       if (x^n+x+1).is_irreducible():
           print(n)
# Joerg Arndt, Mar 02 2016

Extensions

a(1) and a(2) from Eric M. Schmidt, Feb 10 2014

a(22) and a(23) from Joerg Arndt, Mar 02 2016