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Search: id:A057496
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| A057496 |
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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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1
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| 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
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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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
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FORMULA
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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
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MATHEMATICA
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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} ]
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CROSSREFS
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Sequence in context: A145018 A018910 A022936 this_sequence A057708 A032686 A074300
Adjacent sequences: A057493 A057494 A057495 this_sequence A057497 A057498 A057499
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KEYWORD
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nonn
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AUTHOR
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Robert G. Wilson v (rgwv(AT)rgwv.com), Sep 27 2000
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EXTENSIONS
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a(17) - a(20) from Robert G. Wilson v (rgwv(AT)rgwv.com), Mar 11 2007
a(21) - a(24) computed by Richard Brent, Mar 11, 2007, communicated by Gove Effinger
a(25) - a(32) computed by Richard Brent, Mar 16, 2007, communicated by Gove Effinger
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