A123399 Orders of "Gray" fields.

1, 2, 3, 5, 6, 9, 11, 14, 23, 26, 29, 30, 33, 35, 39, 41, 51, 53, 65, 69, 74, 81, 83, 86, 89, 90, 95, 105, 113, 119, 131, 135, 146, 155, 158, 173, 179, 183, 189, 191, 209, 210, 221, 230, 231, 233, 239, 243, 245, 251, 254, 261, 273, 281, 293, 299, 303, 306, 309, 323, 326, 329, 330, 359, 371, 375, 386, 398, 411, 413, 419

Offset

1,2

Comments

Numbers n such that there is a type-2 optimal normal basis over GF(2) and the corresponding polynomial is primitive. Subsequence of A054639. [Joerg Arndt, Apr 28 2012]

References

D. E. Knuth, The Art of Computer Programming, Section 7.2.1.1, Problem 31.

Links

Joerg Arndt, Table of n, a(n) for n = 1..133

Formula

Let c_1(x) = x+1, c_2(x) = x^2+x+1, c_{j+1}(x) = x*c_j(x) + c_{j-1}(x) be polynomials over GF(2). Then n is in the sequence iff c_n(x) is a primitive irreducible polynomial.

Crossrefs

Cf. A054639.

Sequence in context: A008747 A327516 A054639 * A239010 A104738 A319469

Adjacent sequences: A123396 A123397 A123398 * A123400 A123401 A123402

Keyword

nonn

Author

N. J. A. Sloane, Oct 15 2006

Extensions

Terms >=105 by Joerg Arndt, Apr 28 2012.

Status

approved