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A223938 Numbers n such that the trinomial x^n-x-1 is irreducible over GF(3). 2

%I

%S 2,3,4,5,6,13,14,17,30,40,41,51,54,73,121,137,364,446,485,638,925,

%T 1382,1478,2211,2726,5581,5678,6424,8524,10649,15990,17174,18685,18889

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

%t Reap[ Do[ If[ Factor[x^n - x - 1, Modulus -> 3][[0]] =!= Times, Print[n]; Sow[n]], {n, 2, 3000}]][[2, 1]] (* _Jean-Fran├žois Alcover_, Apr 03 2013 *)

%t Select[Range[1000], IrreduciblePolynomialQ[x^# - x - 1, Modulus -> 3] &] (* _Robert Price_, Sep 19 2018 *)

%o (Sage)

%o P.<x> = GF(3)[]

%o for n in range(10^6):

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

%o print(n)

%o (PARI)

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

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

%K nonn,more

%O 1,1

%A _Joerg Arndt_, Mar 29 2013

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Last modified September 24 11:16 EDT 2021. Contains 347642 sequences. (Running on oeis4.)