A389667 Decimal expansion of Sum_{k>=1} (zeta(2*k+1)-1)/(2*k+3).

0, 4, 6, 8, 4, 5, 5, 6, 7, 3, 5, 1, 9, 4, 7, 8, 6, 6, 6, 6, 1, 3, 7, 3, 9, 2, 2, 0, 9, 1, 2, 1, 6, 2, 8, 6, 7, 5, 3, 4, 5, 7, 3, 9, 3, 5, 0, 2, 8, 2, 7, 6, 0, 6, 0, 0, 4, 6, 9, 2, 9, 7, 0, 9, 1, 0, 2, 9, 4, 5, 4, 7, 4, 2, 2, 7, 7, 6, 7, 3, 9, 6, 9, 9, 0, 3, 5, 7, 8, 1, 4, 0, 6, 1, 9, 0, 8, 9, 5, 3, 1, 4, 0, 3, 4, 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. (2.18), p. 389.

Formula

Equals 13/12 - gamma/3 - log(2)/2 - 2*log(A), where gamma is Euler's constant (A001620), and A is the Glaisher-Kinkelin constant (A074962).

Example

0.046845567351947866661373922091216286753457393502827...

Mathematica

RealDigits[13/12 - EulerGamma/3 - Log[2]/2 - 2 Log[Glaisher], 10, 120, -1][[1]]

Prog

(PARI) 11/12 - Euler/3 - log(2)/2 + 2 * zeta'(-1)

Crossrefs

Cf. A001620, A074962, A225746.

Related constants: A321943, A379425, A389666, A389668, A389669, A389670.

Sequence in context: A179022 A021685 A071851 * A083256 A083257 A286366

Adjacent sequences: A389664 A389665 A389666 * A389668 A389669 A389670

Keyword

nonn,cons

Author

Amiram Eldar, Oct 10 2025

Status

approved