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%I #5 Apr 30 2013 12:15:32
%S 1,-13,36,-258,5622,-31716,-83460,1766388,-2952900,59171652,
%T -2614259136,25907667528,-87008484996,410147565360,-10353918172170,
%U 73320103253412,409638469731702,-7210516315882284,18236866211886120,-161388385633551558,6594430509454957926
%N Numerators of the convolutory inverse of the primes of the form 6m+1.
%C Coefficients in 1/(1+g(x)), where g is the generating functions of the sequence of primes (7,13,19,31,37,...) of primes congruent to 1 mod 6. For the convolutory inverse of the primes, see A030018. Conjecture: a(n+1)/a(n) diverges.
%H Clark Kimberling, <a href="/A225131/b225131.txt">Table of n, a(n) for n = 1..1000</a>
%e (7,13,19,31,37,...)**(1/7, -13/49, 36/343, -258/2401, 5622/16807,...) = (1,0,0,0,0,...), where ** denotes convolution.
%t q = {}; Do[If[PrimeQ[p = 6*n - 1], AppendTo[q, p]], {n, 0, 15000}]; r[n_] := q[[n]]; k[n_] := k[n] = 0; k[1] = 1; s[n_] := s[n] = (k[n] - Sum[r[k]*s[n - k + 1], {k, 2, n}])/r[1]; t = Table[s[n], {n, 1, 40}]; Numerator[t]
%Y Cf. A030018, A225127, A225130.
%K sign,easy
%O 1,2
%A _Clark Kimberling_, Apr 29 2013