A223938 Numbers n such that the trinomial x^n-x-1 is irreducible over GF(3).

2, 3, 4, 5, 6, 13, 14, 17, 30, 40, 41, 51, 54, 73, 121, 137, 364, 446, 485, 638, 925, 1382, 1478, 2211, 2726, 5581, 5678, 6424, 8524, 10649, 15990, 17174, 18685, 18889, 27461, 29523, 30677, 39641, 42038, 58566, 71380, 72781, 82493

Offset

1,1

Comments

Any subsequent terms are > 10^5. - Lucas A. Brown, Dec 11 2022

Links

Table of n, a(n) for n=1..43.

Mathematica

Reap[ Do[ If[ Factor[x^n - x - 1, Modulus -> 3][[0]] =!= Times, Print[n]; Sow[n]], {n, 2, 3000}]][[2, 1]] (* Jean-François Alcover, Apr 03 2013 *)
Select[Range[1000], IrreduciblePolynomialQ[x^# - x - 1, Modulus -> 3] &] (* Robert Price, Sep 19 2018 *)

Prog

(Sage)
P.<x> = GF(3)[]
for n in range(10^6):
       if (x^n-x-1).is_irreducible():
           print(n)
(PARI)
for (n=1, 10^6, if ( polisirreducible(Mod(1, 3)*(x^n-x-1)), print1(n, ", ") ) );

Crossrefs

Cf. A002475 (n such that x^n-x-1 is irreducible over GF(2)).

Sequence in context: A171597 A086185 A072564 * A222194 A057224 A153695

Adjacent sequences: A223935 A223936 A223937 * A223939 A223940 A223941

Keyword

nonn,more

Author

Joerg Arndt, Mar 29 2013

Extensions

a(35)-a(43) from Lucas A. Brown, Dec 11 2022

Status

approved