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Numbers n such that x^n + x^3 + x^2 + x + 1 is irreducible over GF(2).
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%I #23 May 11 2021 09:45:55

%S 1,2,3,4,5,7,10,17,20,25,28,31,41,52,130,151,196,503,650,761,986,1391,

%T 2047,6172,6431,6730,8425,10162,11410,12071,13151,14636,17377,18023,

%U 32770,77047,102842,130777,137113,143503,168812,192076

%N Numbers n such that x^n + x^3 + x^2 + x + 1 is irreducible over GF(2).

%C 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

%C 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

%F 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

%Y Cf. A002475.

%Y Other than the term 3, subsequence of A057461.

%K nonn

%O 1,2

%A _Robert G. Wilson v_, Sep 27 2000

%E a(20)-a(23) from _Robert G. Wilson v_, Mar 11 2007

%E a(24)-a(27) computed by _Richard P. Brent_, Mar 11 2007, communicated by Gove Effinger

%E a(27)-a(35) computed by _Richard P. Brent_, Mar 16 2007, communicated by Gove Effinger

%E a(36)-a(42) computed by Jonathan Webster, Feb 18 2010

%E 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