A335707 Decimal expansion of Sum_{primes p} log(p) / (p^2 + p - 1).

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

Offset: 0

Author

Vaclav Kotesovec, Jun 18 2020

Keywords

• nonn
• cons

Examples

			0.41875757879412548053442125602870463613655516544928702940522...
		

Links

• Steven R. Finch, Mathematical Constants II, Encyclopedia of Mathematics and Its Applications, Cambridge University Press, Cambridge, 2018, p. 100, p. 169.

Crossrefs

Cf. A062355, A085609.

Programs

Mathematica

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