A225131 Numerators of the convolutory inverse of the primes of the form 6m+1.

1, -13, 36, -258, 5622, -31716, -83460, 1766388, -2952900, 59171652, -2614259136, 25907667528, -87008484996, 410147565360, -10353918172170, 73320103253412, 409638469731702, -7210516315882284, 18236866211886120, -161388385633551558, 6594430509454957926

Offset: 1

Author

Clark Kimberling, Apr 29 2013

Keywords

• sign
• easy

Comments

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.

Examples

			(7,13,19,31,37,...)**(1/7, -13/49, 36/343, -258/2401, 5622/16807,...) = (1,0,0,0,0,...), where ** denotes convolution.
		

Links

• Clark Kimberling, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A030018, A225127, A225130.

Programs

Mathematica

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]