A256923 Decimal expansion of Sum_{k>=1} (zeta(2k)/k)*(1/3)^(2k).

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

Offset

0,2

References

H. M. Srivastava and Junesang Choi, Zeta and q-Zeta Functions and Associated Series and Integrals, Elsevier Insights (2011) p. 272.

Links

Table of n, a(n) for n=0..104.

Eric Weisstein's MathWorld, Riemann Zeta Function

Wikipedia, Riemann Zeta Function

Formula

Equals log(Gamma(2/3)*Gamma(4/3)).

Equals log(2*Pi/(3*sqrt(3))).

Equals log(A248897).

Equals -Sum_{k>=1} log(1 - 1/(3*k)^2). - Amiram Eldar, Aug 12 2020

Example

0.189958633407180946467791617427446722751559110541442648...

Mathematica

RealDigits[Log[2*Pi/(3*Sqrt[3])], 10, 105] // First

Crossrefs

Cf. A073006, A202623, A248897, A256924.

Sequence in context: A345987 A241990 A358519 * A347219 A320304 A217292

Adjacent sequences: A256920 A256921 A256922 * A256924 A256925 A256926

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Apr 13 2015

Status

approved