OFFSET
0,2
FORMULA
Equals Sum_{k>=2} (k^5 - 3*k^4 + k^3 - k^2 + k - 1)/(k*(k^6 - 1)).
Equals 1/3 - 2*gamma/3 - (2/3)*Re(Psi(1/2 + i*sqrt(3)/2)), where Psi is the digamma function, gamma is the Euler-Mascheroni constant (see A001620), and i=sqrt(-1).
Equals 1/3 - 2*gamma/3 + 2*A339135/3 - 4*log(2)/9.
Equals Sum_{k>=2} 1/(k*(k^3 - 1)). - Vaclav Kotesovec, Dec 24 2020
EXAMPLE
0.09180726255210907564327636663...
MATHEMATICA
Join[{0}, RealDigits[Chop[N[Sum[Zeta[3 n + 1] - 1, {n, 1, Infinity}], 105]]][[1]]]
PROG
(PARI) suminf(k=1, zeta(3*k+1)-1) \\ Michel Marcus, Dec 09 2020
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Artur Jasinski, Dec 09 2020
STATUS
approved