A225130 Numerators of the convolutory inverse of the primes of the form 6m-1.

1, -11, 36, -36, 36, -3786, 63786, -405036, 1215036, -4368786, 45022536, -380988786, 2242736286, -7681046286, 26949825036, -435049072536, 4543990507536, -25626723348786, 80068989783786, -100028016375036, 1579550678122536, -31186023693776286, 252408733196148786

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 (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....

Examples

			(5,11,17,23,29,...)**(1/5, -11/25, 36/125, -36/625, 36/3125,...) = (1,0,0,0,0,...), where ** denotes convolution.
		

Links

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

Crossrefs

Cf. A030018, A225127, A225131.

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]