A256318 Decimal expansion of Sum_{k>=0} zeta(2k)/((2k+1)*4^(2k)) (negated).

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

Offset

0,1

Links

G. C. Greubel, Table of n, a(n) for n = 0..10000

H. M. Srivasata, M. L. Glasser, and Victor S. Adamchik, Some Definite Integrals Associated with the Riemann Zeta Function

Formula

Equals -G/Pi - log(2)/4 = -A143233-A379101, where G is Catalan's constant.

Example

-0.464847699170805107492692486832939060882941187575901...

Mathematica

RealDigits[-Catalan/Pi - Log[2]/4, 10, 105] // First

Prog

(PARI) Catalan/Pi + log(2)/4 \\ Charles R Greathouse IV, Mar 23 2015
(PARI) .5 - sumpos(k=1, zeta(2*k)/(2*k+1)/16^k) \\ Charles R Greathouse IV, Mar 23 2015
(Magma) SetDefaultRealField(RealField(100)); R:=RealField(); Catalan(R)/Pi(R) + Log(2)/4; // G. C. Greubel, Aug 25 2018

Crossrefs

Cf. A006752, A256319.

Sequence in context: A084892 A344475 A245556 * A018835 A055166 A202243

Adjacent sequences: A256315 A256316 A256317 * A256319 A256320 A256321

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Mar 23 2015

Status

approved