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 A225128 Numerators of the convolutory inverse of the primes of the form 4m+3. 2

%I

%S 1,-7,16,-52,412,-2068,6964,-19960,81880,-396844,1448908,-3853348,

%T 9668860,-45544768,238303744,-764868256,1962327904,-9820441204,

%U 62744531956,-306405293056,1228176071080,-5276516025688,26307346186816,-126143746044604,534479888324932

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

%C 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 Clark Kimberling, <a href="/A225128/b225128.txt">Table of n, a(n) for n = 1..1000</a>

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

%t 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 Cf. A030018, A225127, A225129.

%K sign,easy

%O 1,2

%A _Clark Kimberling_, Apr 29 2013

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Last modified August 12 05:33 EDT 2020. Contains 336438 sequences. (Running on oeis4.)