A345308 Decimal expansion of Sum_{p primes} log(p) / (p-1)^2.

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

Offset

1,2

Links

Table of n, a(n) for n=1..105.

Steven R. Finch, Mathematical Constants II, Encyclopedia of Mathematics and Its Applications, Cambridge University Press, Cambridge, 2018, p. 156 (constant C10 + 1).

Eric Weisstein's World of Mathematics, Prime Factor, formula (13)-(14), (constant U).

Example

1.226968805653470005965662568745762562988257454901426311714794620109...

Mathematica

ratfun = 1/((p - 1)^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, 25}]; Do[Print[N[Sum[Log[p]*ratfun /. p -> Prime[k], {k, 1, m}] + zetas, 110]], {m, 1000, 5000, 1000}]

Crossrefs

Cf. A138312, A306016, A345364.

Sequence in context: A094485 A331988 A242978 * A231137 A371400 A188808

Adjacent sequences: A345305 A345306 A345307 * A345309 A345310 A345311

Keyword

nonn,cons

Author

Vaclav Kotesovec, Jun 13 2021

Status

approved