A335706 Decimal expansion of Sum_{primes p} 2*p*(2*p^3 - 9*p^2 - 1) * log(p)^2 / (p^3 + p - 2)^2.

2, 3, 5, 1, 0, 9, 7, 1, 4, 0, 7, 7, 8, 7, 6, 6, 2, 8, 3, 2, 3, 4, 1, 6, 6, 0, 8, 5, 2, 3, 3, 7, 7, 1, 2, 7, 8, 6, 3, 0, 3, 8, 4, 5, 2, 1, 8, 8, 5, 9, 6, 0, 2, 7, 4, 3, 4, 3, 3, 3, 2, 7, 7, 7, 1, 8, 6, 9, 1, 8, 0, 2, 0, 4, 5, 5, 1, 6, 8, 5, 5, 3, 0, 7, 2, 9, 6, 3, 5, 0, 1, 9, 1, 0, 9, 1, 9, 8, 3, 0, 5, 2, 7, 2, 4, 5

Offset

0,1

Links

Table of n, a(n) for n=0..105.

Example

0.23510971407787662832341660852337712786303845218859602743433...

Mathematica

ratfun = 2*p*(2*p^3 - 9*p^2 - 1) / (p^3 + p - 2)^2; zetas = 0; ratab = Table[konfun = Together[Simplify[ratfun - c*(p^power/(p^power - 1)^2)]]; coefs = CoefficientList[Numerator[konfun], p]; sol = Solve[Last[coefs] == 0, c][[1]]; zetas = zetas + c*(-Zeta'[power]^2/Zeta[power]^2 + Zeta''[power]/Zeta[power]) /. sol; ratfun = konfun /. sol, {power, 2, 20}]; Do[Print[N[Sum[Log[p]^2*ratfun /. p -> Prime[k], {k, 1, m}] + zetas, 100]], {m, 2000, 20000, 2000}]

Crossrefs

Cf. A208133, A335705.

Sequence in context: A062007 A031067 A300392 * A339640 A031027 A134730

Adjacent sequences: A335703 A335704 A335705 * A335707 A335708 A335709

Keyword

nonn,cons

Author

Vaclav Kotesovec, Jun 18 2020

Status

approved