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A256318 Decimal expansion of Sum_{k>=0} zeta(2k)/((2k+1)*4^(2k)) (negated). 2
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 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

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

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

FORMULA

Equals -G/Pi - log(2)/4, 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: A199959 A084892 A245556 * A018835 A055166 A202243

Adjacent sequences:  A256315 A256316 A256317 * A256319 A256320 A256321

KEYWORD

nonn,cons,easy

AUTHOR

Jean-Fran├žois Alcover, Mar 23 2015

STATUS

approved

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Last modified August 20 23:38 EDT 2019. Contains 326155 sequences. (Running on oeis4.)