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A071802
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Table in which n-th row gives exponents (in decreasing order) of lexicographically earliest primitive irreducible polynomial of degree n over GF(2).
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0
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1, 0, 2, 1, 0, 3, 1, 0, 4, 1, 0, 5, 2, 0, 6, 1, 0, 7, 1, 0, 8, 4, 3, 1, 0, 9, 1, 0, 10, 3, 0, 11, 2, 0, 12, 3, 0, 13, 4, 3, 1, 0, 14, 5, 0, 15, 1, 0, 16, 5, 3, 1, 0, 17, 3, 0, 18, 3, 0, 19, 5, 2, 1, 0, 20, 3, 0, 21, 2, 0, 22, 1, 0, 23, 5, 0, 24, 4, 3, 1, 0, 25, 3, 0, 26, 4, 3, 1, 0, 27, 5, 2, 1, 0
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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REFERENCES
| F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North Holland, 1978, p. 408.
M. Olofsson, VLSI Aspects on Inversion in Finite Fields, Dissertation No. 731, Dept Elect. Engin., Linkoping, Sweden, 2002.
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EXAMPLE
| x+1, x^2+x+1, x^3+x+1, x^4+x+1, x^5+x^2+1, ...
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MATHEMATICA
| a = {}; Do[k = 2^n + 1; While[s = Apply[Plus, IntegerDigits[k, 2]*x^Table[i, {i, n, 0, -1}]]; k < 2^(n + 1) - 1 && Factor[s, Modulus -> 2] =!= s, k += 2]; a = Append[a, Reverse[ Exponent[ Apply[ Plus, IntegerDigits[k, 2]*x^Table[i, {i, n, 0, -1}]], x, List]]], {n, 1, 27}]; Flatten[a]
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CROSSREFS
| Cf. A058943.
Sequence in context: A168016 A029323 A194849 * A110355 A029293 A176808
Adjacent sequences: A071799 A071800 A071801 * A071803 A071804 A071805
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KEYWORD
| nonn,nice,easy,tabf
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Jun 24 2002
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EXTENSIONS
| Extended by Robert G. Wilson v (rgwv(AT)rgwv.com), Jun 25 2002
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