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

%I A223938 #29 Dec 12 2022 01:48:48
%S A223938 2,3,4,5,6,13,14,17,30,40,41,51,54,73,121,137,364,446,485,638,925,
%T A223938 1382,1478,2211,2726,5581,5678,6424,8524,10649,15990,17174,18685,
%U A223938 18889,27461,29523,30677,39641,42038,58566,71380,72781,82493
%N A223938 Numbers n such that the trinomial x^n-x-1 is irreducible over GF(3).
%C A223938 Any subsequent terms are > 10^5. - _Lucas A. Brown_, Dec 11 2022
%t A223938 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 *)
%t A223938 Select[Range[1000], IrreduciblePolynomialQ[x^# - x - 1, Modulus -> 3] &] (* _Robert Price_, Sep 19 2018 *)
%o A223938 (Sage)
%o A223938 P.<x> = GF(3)[]
%o A223938 for n in range(10^6):
%o A223938        if (x^n-x-1).is_irreducible():
%o A223938            print(n)
%o A223938 (PARI)
%o A223938 for (n=1, 10^6, if ( polisirreducible(Mod(1, 3)*(x^n-x-1)), print1(n, ", ") ) );
%Y A223938 Cf. A002475 (n such that x^n-x-1 is irreducible over GF(2)).
%K A223938 nonn,more
%O A223938 1,1
%A A223938 _Joerg Arndt_, Mar 29 2013
%E A223938 a(35)-a(43) from _Lucas A. Brown_, Dec 11 2022