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%I #29 Dec 12 2022 01:48:48
%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,
%U 18889,27461,29523,30677,39641,42038,58566,71380,72781,82493
%N Numbers n such that the trinomial x^n-x-1 is irreducible over GF(3).
%C Any subsequent terms are > 10^5. - _Lucas A. Brown_, Dec 11 2022
%t 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 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
%E a(35)-a(43) from _Lucas A. Brown_, Dec 11 2022
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