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

%I #21 Apr 17 2020 07:41:12

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

%T 3627,9247,9955

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

%C No other n < 4400. - _Michael Somos_, Mar 12 2007

%C Next term > 10^4. [_Joerg Arndt_, Mar 02 2016]

%o (PARI) isok(n) = polisirreducible(Mod(1, 5)*(x^n + x + 1)); \\ _Michel Marcus_, Feb 11 2014

%o (Sage)

%o P.<x> = GF(5)[]

%o for n in range(0, 10000):

%o if (x^n+x+1).is_irreducible():

%o print(n)

%o # _Joerg Arndt_, Mar 02 2016

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

%K nonn,more

%O 1,3

%A _Robert G. Wilson v_, Dec 13 2000

%E a(1) and a(2) from _Eric M. Schmidt_, Feb 10 2014

%E a(22) and a(23) from _Joerg Arndt_, Mar 02 2016