A225128 -id:A225128 - cp's OEIS frontend

A225129 Numerators of the convolutory inverse of the primes of the form 4m+1.

1, -13, 84, -712, 6916, -55788, 432584, -3555212, 28927916, -229458788, 1847086584, -14858027212, 118242773916, -945499611788, 7556178053084, -60048635124212, 477995366994916, -3810212526827288, 30296614848644584, -240796293647346212, 1916211884628153416

Offset: 1

Clark Kimberling, Apr 29 2013

Coefficients in 1/(1+g(x)), where g is the generating functions of the sequence of primes (5,13,17,29,37,...) of primes congruent to 1 mod 4. For the convolutory inverse of the primes, see A030018. Conjecture: a(n+1)/a(n) -> -1.59045463062282....

			(5,13,17,29,37,...)**(1/5, -13/25, 84/125, -712/625, 6916/3125,...) = (1,0,0,0,0,...), where ** denotes convolution.

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

Cf. A030018, A225127, A225128.

q = {}; Do[If[PrimeQ[p = 4*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]

cp's OEIS Frontend

A225129 Numerators of the convolutory inverse of the primes of the form 4m+1.

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