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A223938 Numbers n such that the trinomial x^n-x-1 is irreducible over GF(3). 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..34.

MATHEMATICA

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 *)

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: A115307 A171597 A086185 * A222194 A057224 A153695

Adjacent sequences:  A223935 A223936 A223937 * A223939 A223940 A223941

KEYWORD

nonn,more

AUTHOR

Joerg Arndt, Mar 29 2013

STATUS

approved

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Last modified January 18 19:19 EST 2020. Contains 331029 sequences. (Running on oeis4.)