A339606 Decimal expansion of Sum_{k>=0} (zeta(3*k+2)-1).

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

Offset

0,1

Links

Table of n, a(n) for n=0..104.

Formula

Equals Sum_{k>=1} 1/(k^3 + 1).

Equals -1/3 + gamma/3 + (1/3)*Re(Psi(1/2 + i*sqrt(3)/2)) + sqrt(3)*Pi*tanh(sqrt(3)*Pi/2)/6, where Psi is digamma function, gamma is Euler-Mascheroni constant (see A001620), and i=sqrt(-1).

Equals -1/3 + gamma/3 - (1/3)*A339135 + 2*log(2)/9 + sqrt(3)*Pi*tanh(sqrt(3)*Pi/2)/6.

Equals 1 - A339605 - A339604.

Equals 1/2 + Sum_{k>=1} (-1)^(k+1) * (zeta(3*k)-1). - Amiram Eldar, Jan 07 2024

Example

0.6865033423386238859646...

Maple

evalf(Re(sum(1/(k^3+1), k=1..infinity)), 120);  # Alois P. Heinz, Dec 12 2020

Mathematica

RealDigits[Chop[N[Sum[Zeta[3 n + 2] - 1, {n, 0, Infinity}], 105]]][[1]]

Prog

(PARI) suminf(k=0, zeta(3*k+2)-1) \\ Michel Marcus, Dec 09 2020

Crossrefs

Cf. A024006, A256919, A338815, A339135, A339529, A339530, A339604, A339605.

Sequence in context: A021597 A331941 A169685 * A360928 A200326 A088751

Adjacent sequences: A339603 A339604 A339605 * A339607 A339608 A339609

Keyword

nonn,cons

Author

Artur Jasinski, Dec 09 2020

Status

approved