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

Author

Joerg Arndt, Mar 29 2013

Keywords

• nonn
• more

Comments

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

Crossrefs

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

Programs

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 *)

PARI

for (n=1, 10^6, if ( polisirreducible(Mod(1, 3)*(x^n-x-1)), print1(n, ", ") ) );

Sage

P. = GF(3)[]
for n in range(10^6):
       if (x^n-x-1).is_irreducible():
           print(n)

Extensions

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