

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
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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


LINKS

Table of n, a(n) for n=1..42.


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



