A255681 Decimal expansion of Sum_{k>=1} zeta(2*k+1)/((2*k+1)*2^(2*k)).

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

Offset

0,3

Links

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

H. M. Srivastava and Junesang Choi, Zeta and q-Zeta Functions and Associated Series and Integrals, Elsevier Insights, 2011, pp. 272 and 314.

Eric Weisstein's MathWorld, Riemann Zeta Function.

Wikipedia, Riemann Zeta Function.

Formula

Equals log(2) - EulerGamma.

Equals Sum_{k>=1} (zeta(2*k+1)-1)/(k+1). - Amiram Eldar, May 24 2021

Equals Sum_{k>=1} psi(k)/2^k, where psi(x) is the digamma function. - Amiram Eldar, Sep 12 2022

Example

0.1159315156584124488107200313757741370333407984203316553149...

Mathematica

RealDigits[Log[2] - EulerGamma, 10, 105] // First

Prog

(PARI) default(realprecision, 100); log(2) - Euler \\ G. C. Greubel, Sep 06 2018
(Magma) SetDefaultRealField(RealField(100)); R:= RealField(); Log(2) - EulerGamma(R); // G. C. Greubel, Sep 06 2018

Crossrefs

Cf. A001620, A002162, A094642 (= log(Pi/2) = Sum_{k>=2} zeta(2*k)/(k*2^(2*k))).

Sequence in context: A111698 A216755 A344149 * A021948 A306883 A333155

Adjacent sequences: A255678 A255679 A255680 * A255682 A255683 A255684

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Apr 13 2015

Status

approved