cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A225128 #6 Apr 30 2013 12:09:09
%S A225128 1,-7,16,-52,412,-2068,6964,-19960,81880,-396844,1448908,-3853348,
%T A225128 9668860,-45544768,238303744,-764868256,1962327904,-9820441204,
%U A225128 62744531956,-306405293056,1228176071080,-5276516025688,26307346186816,-126143746044604,534479888324932
%N A225128 Numerators of the convolutory inverse of the primes of the form 4m+3.
%C A225128 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....
%H A225128 Clark Kimberling, <a href="/A225128/b225128.txt">Table of n, a(n) for n = 1..1000</a>
%e A225128 (3,7,11,19,23,...)**(1/3, -7/9, 16/27, -52/81, 412/243,...) = (1,0,0,0,0,...), where ** denotes convolution.
%t A225128 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]
%Y A225128 Cf. A030018, A225127, A225129.
%K A225128 sign,easy
%O A225128 1,2
%A A225128 _Clark Kimberling_, Apr 29 2013