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

Author

N. J. A. Sloane, Oct 15 2006

Keywords

• nonn

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

Crossrefs

Cf. A054639.

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.

Extensions

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