%I #2 Mar 30 2012 17:34:34
%S 1,0,-1,0,1,-1,-1,1,1,-1,-1,1,1,-2,-1,4,0,-5,3,5,-7,-4,10,1,-12,2,16,
%T -6,-21,13,27,-29,-28,52,19,-77,4,97,-40,-110,85,119,-143,-119,230,95,
%U -354,-16,499,-159,-622
%N Coefficients of the polynomial from factoring (x^167+1)/(x+1) modulo 2 gives: p(x)=1 + x + x^4 + x^6 + x^8 + x^10 + x^12 + x^13 + x^17 + x^19 + x^23 + x^24 + x^25 + x^26 + x^27 + x^29 + x^31 + x^32 + x^33 + x^35 + x^36 + x^40 + x^42 + x^45 + x^46 + x^47 + x^49 + x^50 + x^52 + x^53 + x^56 + x^59 + x^60 + x^62 + x^64 + x^67 + x^70 + x^71 + x^73 + x^76 + x^78 + x^81 + x^83.
%C Primes of the type 11,23,83,107,167...
%C Flatten[Table[If[PrimeQ[n] && PrimeQ[10*n - 1] && PrimeQ[( n - 1)/2], n, {}], {n, 1, 10000}]]
%C that gives nearly equal factorizations:
%C Factor[(x^Prime+1)/(x+1),Modulus->2]=f1(x)*f2(x);
%C and the power of factor is the next lower prime:
%C 23->11;
%C 167->83
%F p(x)=1 + x + x^4 + x^6 + x^8 + x^10 + x^12 + x^13 + x^17 +
%F x^19 + x^23 + x^24 + x^25 + x^26 + x^27 + x^29 + x^31 +
%F x^32 + x^33 + x^35 + x^36 + x^40 + x^42 + x^45 + x^46 +
%F x^47 + x^49 + x^50 + x^52 + x^53 + x^56 + x^59 + x^60 +
%F x^62 + x^64 + x^67 + x^70 + x^71 + x^73 + x^76 + x^78 +
%F x^81 + x^83;
%F a(n)=coefficients(1/(x^83*p(1/x)))
%t f[x_] = FactorList[PolynomialMod[(x^167 + 1)/((x + 1)), 2], Modulus -> 2][[2]][[1]];
%t g[x] = ExpandAll[x^83*f[1/x]];
%t a = Table[SeriesCoefficient[ Series[1/g[x], {x, 0, 50}], n], {n, 0, 50}]
%K sign,uned
%O 0,14
%A _Roger L. Bagula_, Mar 11 2009