

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
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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

Other than the term 3, subsequence of A057461.


KEYWORD

nonn


AUTHOR



EXTENSIONS

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



