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A058334
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Numbers n such that the trinomial x^n + x + 1 is irreducible over GF(5).
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1
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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
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1,3
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COMMENTS
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No other n < 4400. - Michael Somos, Mar 12 2007
Next term > 10^4. [Joerg Arndt, Mar 02 2016]
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LINKS
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Table of n, a(n) for n=1..23.
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MATHEMATICA
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Do[ If[ ToString[ Factor[ x^n + x^1 + 1, Modulus -> 5] ] == ToString[ x^n + x^1 + 1], Print[n] ], {n, 0, 750} ]
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PROG
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(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
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CROSSREFS
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Cf. A002475 (GF(2)), A058857 (GF(7)).
Sequence in context: A195530 A295509 A225747 * A303090 A131093 A002864
Adjacent sequences: A058331 A058332 A058333 * A058335 A058336 A058337
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KEYWORD
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nonn,more,changed
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AUTHOR
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Robert G. Wilson v, Dec 13 2000
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EXTENSIONS
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a(1) and a(2) from Eric M. Schmidt, Feb 10 2014
a(22) and a(23) from Joerg Arndt, Mar 02 2016
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STATUS
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approved
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