A256922 Decimal expansion of Sum_{k>=2} (-1)^k*zeta(k)/(k*2^k).

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

Offset: 0

Author

Jean-François Alcover, Apr 13 2015

Keywords

• nonn
• cons
• easy

Examples

			0.167825594815521207957737599259554003269226940067362331039...
		

References

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

Links

• G. C. Greubel, Table of n, a(n) for n = 0..10000
• Eric Weisstein's MathWorld, Riemann Zeta Function
• Wikipedia, Riemann Zeta Function

Crossrefs

Cf. A001620, A002162, A053510, A094640, A256921.

Programs

Magma

SetDefaultRealField(RealField(100)); R:= RealField(); EulerGamma(R)/2 + (1/2)*Log(Pi(R)) - Log(2); // G. C. Greubel, Sep 05 2018

Mathematica

RealDigits[EulerGamma/2 + (1/2)*Log[Pi] - Log[2], 10, 105] // First

PARI

Euler/2 + log(Pi)/2 - log(2) \\ Michel Marcus, Apr 13 2015

Formula

Equals A001620/2 + (1/2)*log(Pi) - log(2).

Equals Sum_{k>=1} (1/(2*k) - log(1 + 1/(2*k))). - Amiram Eldar, Jul 22 2020

Equals (A001620 - A094640)/2. - Ruud H.G. van Tol, Apr 26 2025