|
|
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.
|
|
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
|
|
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
|
|
|
|