A389666 Decimal expansion of Sum_{k>=1} (zeta(2*k)-1)/(k+1).

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

Offset

0,1

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. (2.17), p. 388.

Michael I. Shamos, A catalog of the real numbers, 2011. See p. 394.

Formula

Equals 3/2 - log(Pi) (Choi et al., 1995).

Equals -Sum_{k>=2} (k^2 * log(1-1/k^2) + 1) (Shamos, 2011).

Example

0.35527011415059982585657264864694128835270518708468...

Mathematica

RealDigits[3/2 - Log[Pi], 10, 120][[1]]

Prog

(PARI) 3/2 - log(Pi)

Crossrefs

Cf. A061444.

Related constants: A321943, A379425, A389667, A389668, A389669, A389670.

Sequence in context: A387987 A078063 A373304 * A019944 A320477 A110551

Adjacent sequences: A389663 A389664 A389665 * A389667 A389668 A389669

Keyword

nonn,cons,easy

Author

Amiram Eldar, Oct 10 2025

Status

approved