A335705 Decimal expansion of Sum_{primes p} 2*(p-3) * log(p) / (p^3 + p - 2).

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

Offset

0,1

Links

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

Example

0.079339315977982136748150057589344450315501605856610561211269...

Mathematica

ratfun = 2*(p-3) / (p^3 + p - 2); 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}]

Crossrefs

Cf. A208133, A306072, A335706.

Sequence in context: A011345 A201770 A086282 * A156000 A019804 A021130

Adjacent sequences: A335702 A335703 A335704 * A335706 A335707 A335708

Keyword

nonn,cons

Author

Vaclav Kotesovec, Jun 18 2020

Status

approved