|
| |
|
|
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; 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
|
|
|
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: A107586 A206737 A130080 * A191864 A180348 A001729
Adjacent sequences: A057493 A057494 A057495 * A057497 A057498 A057499
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Robert G. Wilson v (rgwv(AT)rgwv.com), Sep 27 2000
|
|
|
EXTENSIONS
| a(20) - a(23) from Robert G. Wilson v (rgwv(AT)rgwv.com), Mar 11 2007
a(24) - a(27) computed by Richard Brent, Mar 11, 2007, communicated by Gove Effinger
a(27) - a(35) computed by Richard 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 Wilson and Richard Brent to account for this. Added terms a(36) through a(42). - Jonathan Webster (jwebster(AT)bates.edu), Feb 18 2010
|
| |
|
|
