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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 13 03:41 EST 2019. Contains 329968 sequences. (Running on oeis4.)