

A123399


Orders of "Gray" fields.


1



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
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OFFSET

1,2


COMMENTS

Numbers n such that there is a type2 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_{j1}(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



