OFFSET
0,14
COMMENTS
Primes of the type 11,23,83,107,167...
Flatten[Table[If[PrimeQ[n] && PrimeQ[10*n - 1] && PrimeQ[( n - 1)/2], n, {}], {n, 1, 10000}]]
that gives nearly equal factorizations:
Factor[(x^Prime+1)/(x+1),Modulus->2]=f1(x)*f2(x);
and the power of factor is the next lower prime:
23->11;
167->83
FORMULA
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;
a(n)=coefficients(1/(x^83*p(1/x)))
MATHEMATICA
f[x_] = FactorList[PolynomialMod[(x^167 + 1)/((x + 1)), 2], Modulus -> 2][[2]][[1]];
g[x] = ExpandAll[x^83*f[1/x]];
a = Table[SeriesCoefficient[ Series[1/g[x], {x, 0, 50}], n], {n, 0, 50}]
CROSSREFS
KEYWORD
sign,uned
AUTHOR
Roger L. Bagula, Mar 11 2009
STATUS
approved