A225128 Numerators of the convolutory inverse of the primes of the form 4m+3.

1, -7, 16, -52, 412, -2068, 6964, -19960, 81880, -396844, 1448908, -3853348, 9668860, -45544768, 238303744, -764868256, 1962327904, -9820441204, 62744531956, -306405293056, 1228176071080, -5276516025688, 26307346186816, -126143746044604, 534479888324932

Offset

1,2

Comments

Coefficients in 1/(1+g(x)), where g is the generating functions of the sequence of primes (3,7,11,19,23,31,...) of primes congruent to 3 mod 4. For the convolutory inverse of the primes, see A030018. Conjecture: a(n+1)/a(n) -> -1.370819405....

Links

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

Example

(3,7,11,19,23,...)**(1/3, -7/9, 16/27, -52/81, 412/243,...) = (1,0,0,0,0,...), where ** denotes convolution.

Mathematica

q = {}; Do[If[PrimeQ[p = 4*n + 3], 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, A225129.

Sequence in context: A152530 A065099 A001345 * A056613 A318413 A342873

Adjacent sequences: A225125 A225126 A225127 * A225129 A225130 A225131

Keyword

sign,easy

Author

Clark Kimberling, Apr 29 2013

Status

approved