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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, 27461, 29523, 30677, 39641, 42038, 58566, 71380, 72781, 82493 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Any subsequent terms are > 10^5. - Lucas A. Brown, Dec 11 2022
LINKS
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 *)
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: A171597 A086185 A072564 * A222194 A057224 A153695
KEYWORD
nonn,more
AUTHOR
Joerg Arndt, Mar 29 2013
EXTENSIONS
a(35)-a(43) from Lucas A. Brown, Dec 11 2022
STATUS
approved

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Last modified February 25 06:40 EST 2024. Contains 370310 sequences. (Running on oeis4.)