

A058334


Numbers n such that the trinomial x^n + x + 1 is irreducible over GF(5).


1



0, 1, 2, 3, 7, 18, 22, 27, 31, 78, 94, 115, 171, 402, 438, 507, 1363, 1467, 2263, 2283, 3627, 9247, 9955
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OFFSET

1,3


COMMENTS

No other n < 4400.  Michael Somos, Mar 12 2007
Next term > 10^4. [Joerg Arndt, Mar 02 2016]


LINKS

Table of n, a(n) for n=1..23.


MATHEMATICA

Do[ If[ ToString[ Factor[ x^n + x^1 + 1, Modulus > 5] ] == ToString[ x^n + x^1 + 1], Print[n] ], {n, 0, 750} ]


PROG

(PARI) isok(n) = polisirreducible(Mod(1, 5)*(x^n + x + 1)); \\ Michel Marcus, Feb 11 2014
(Sage)
P.<x> = GF(5)[]
for n in range(0, 10000):
if (x^n+x+1).is_irreducible():
print(n)
# Joerg Arndt, Mar 02 2016


CROSSREFS

Cf. A002475 (GF(2)), A058857 (GF(7)).
Sequence in context: A195530 A295509 A225747 * A303090 A131093 A002864
Adjacent sequences: A058331 A058332 A058333 * A058335 A058336 A058337


KEYWORD

nonn,more,changed


AUTHOR

Robert G. Wilson v, Dec 13 2000


EXTENSIONS

a(1) and a(2) from Eric M. Schmidt, Feb 10 2014
a(22) and a(23) from Joerg Arndt, Mar 02 2016


STATUS

approved



