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A123399
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Orders of "Gray" fields.
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1
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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
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1,2
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COMMENTS
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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]
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REFERENCES
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D. E. Knuth, The Art of Computer Programming, Section 7.2.1.1, Problem 31.
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LINKS
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FORMULA
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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.
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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