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 A057496 Numbers n such that x^n + x^3 + x^2 + x + 1 is irreducible over GF(2). 0
 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 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 MATHEMATICA Do[ If[ ToString[ Factor[ x^n + x^3 + x^2 + x + 1, Modulus -> 2 ] ] == ToString[ x^n + x^3 + x^2 + x + 1 ], Print[ n ] ], {n, 0, 750} ] CROSSREFS Sequence in context: A282502 A212463 A130080 * A191864 A180348 A001729 Adjacent sequences:  A057493 A057494 A057495 * A057497 A057498 A057499 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 March 30 10:31 EDT 2020. Contains 333125 sequences. (Running on oeis4.)