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A057496 Numbers n such that x^n + x^3 + x^2 + x + 1 is irreducible over GF(2). 7
1, 2, 3, 4, 5, 7, 10, 17, 20, 25, 28, 31, 41, 52, 130, 151, 196, 503, 650, 761, 986, 1391, 2047, 6172, 6431, 6730, 8425, 10162, 11410, 12071, 13151, 14636, 17377, 18023, 32770, 77047, 102842, 130777, 137113, 143503, 168812, 192076 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
If x^n + x^3 + x^2 + x + 1 is irreducible, then so is its "twin" x^n + x^3 + 1. - Gove Effinger, Mar 11 2007
No term other than 3 can be a multiple of 3, since for m > 1, x^(3*m) + x^3 + x^2 + x + 1 is divisible by x^2 + x + 1. - Jianing Song, May 11 2021
LINKS
FORMULA
Using probabilistic arguments it appears that there should be about 6.5 terms in this sequence with any given number of decimal digits d. - Gove Effinger, Mar 11 2007
CROSSREFS
Cf. A002475.
Other than the term 3, subsequence of A057461.
Sequence in context: A282502 A212463 A130080 * A345663 A191864 A180348
KEYWORD
nonn
AUTHOR
Robert G. Wilson v, Sep 27 2000
EXTENSIONS
a(20)-a(23) from Robert G. Wilson v, Mar 11 2007
a(24)-a(27) computed by Richard P. Brent, Mar 11 2007, communicated by Gove Effinger
a(27)-a(35) computed by Richard P. Brent, Mar 16 2007, communicated by Gove Effinger
a(36)-a(42) computed by Jonathan Webster, Feb 18 2010
Added entries a(1), a(2), a(3) since x^3 + x^2 + 1, x^3 + x + 1 and x^2 + x + 1 are irreducible over GF(2). Changed the offset for the entries computed by Robert G. Wilson v and Richard P. Brent to account for this. Added terms a(36) through a(42). - Jonathan Webster (jwebster(AT)bates.edu), Feb 18 2010
STATUS
approved

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Last modified July 21 04:02 EDT 2024. Contains 374463 sequences. (Running on oeis4.)