A225130 - OEIS

%I #5 Apr 30 2013 12:13:32

%S 1,-11,36,-36,36,-3786,63786,-405036,1215036,-4368786,45022536,

%T -380988786,2242736286,-7681046286,26949825036,-435049072536,

%U 4543990507536,-25626723348786,80068989783786,-100028016375036,1579550678122536,-31186023693776286,252408733196148786

%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 (5,11,17,23,29,...) of primes congruent to -1 mod 6.  For the convolutory inverse of the primes, see A030018.  Conjecture:  a(n+1)/a(n) -> -1.24066....

%H Clark Kimberling, <a href="/A225130/b225130.txt">Table of n, a(n) for n = 1..1000</a>

%e (5,11,17,23,29,...)**(1/5, -11/25, 36/125, -36/625, 36/3125,...) = (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, A225131.

%K sign,easy

%O 1,2

%A _Clark Kimberling_, Apr 29 2013