A389668 Decimal expansion of Sum_{k>=2} (-1)^k * (zeta(k)-1) / (k+2).

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

Offset

0,2

Links

Table of n, a(n) for n=0..105.

Junesang Choi, H. M. Srivastava, and J. R. Quine, Some series involving the zeta function, Bulletin of the Australian Mathematical Society, Vol. 51, No. 3 (1995), pp. 383-393. See eq. (2.31), p. 391.

Formula

Equals (gamma-1)/3 - log(Pi/2)/2 + 2*log(A), where gamma is Euler's constant (A001620), and A is the Glaisher-Kinkelin constant (A074962).

Example

0.13078948972335204626691240223225435742289520003951...

Mathematica

RealDigits[(EulerGamma - 1)/3 - Log[Pi/2]/2 + 2*Log[Glaisher], 10, 120][[1]]

Prog

(PARI) Euler/3 - 1/6 - log(Pi/2)/2 - 2*zeta'(-1)

Crossrefs

Cf. A001620, A074962, A225746.

Related constants: A321943, A379425, A389666, A389667, A389669, A389670.

Sequence in context: A019970 A342698 A397014 * A239022 A343612 A363502

Adjacent sequences: A389665 A389666 A389667 * A389669 A389670 A389671

Keyword

nonn,cons

Author

Amiram Eldar, Oct 10 2025

Status

approved