

A225131


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


2



1, 13, 36, 258, 5622, 31716, 83460, 1766388, 2952900, 59171652, 2614259136, 25907667528, 87008484996, 410147565360, 10353918172170, 73320103253412, 409638469731702, 7210516315882284, 18236866211886120, 161388385633551558, 6594430509454957926
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


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.


LINKS

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


EXAMPLE

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


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]


CROSSREFS

Cf. A030018, A225127, A225130.
Sequence in context: A034129 A243038 A297303 * A118361 A264908 A281004
Adjacent sequences: A225128 A225129 A225130 * A225132 A225133 A225134


KEYWORD

sign,easy


AUTHOR

Clark Kimberling, Apr 29 2013


STATUS

approved



