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%I #4 Mar 30 2012 17:30:44
%S 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,
%T 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,
%U 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
%N Table in which n-th row gives exponents (in decreasing order) of lexicographically earliest primitive irreducible polynomial of degree n over GF(2).
%D F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North Holland, 1978, p. 408.
%D M. Olofsson, VLSI Aspects on Inversion in Finite Fields, Dissertation No. 731, Dept Elect. Engin., Linkoping, Sweden, 2002.
%e x+1, x^2+x+1, x^3+x+1, x^4+x+1, x^5+x^2+1, ...
%t 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]
%Y Cf. A058943.
%K nonn,nice,easy,tabf
%O 1,3
%A _N. J. A. Sloane_, Jun 24 2002
%E Extended by _Robert G. Wilson v_, Jun 25 2002
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