%I #9 Jan 22 2021 07:37:56

%S 0,0,4,0,9,2,6,9,8,2,9,9,2,8,6,2,8,7,3,0,7,4,7,6,2,0,4,6,8,9,6,4,0,2,

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

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

%N Decimal expansion of Sum_{k>=1} (zeta(8*k)-1).

%F Equals Sum_{k>=2} 1/(k^8 - 1).

%F Equals 15/16 - Pi*coth(Pi)/8 + Pi * (sin(sqrt(2)*Pi) + sinh(sqrt(2)*Pi)) / (4*sqrt(2) * (cos(sqrt(2)*Pi) - cosh(sqrt(2)*Pi))).

%F Equals (1/2)*Sum_{k>=2} 1/(k^4-1) - (1/2)*Sum_{k>=2} 1/(k^4+1) = (A256919-A256920)/2. - _R. J. Mathar_, Jan 22 2021

%e 0.00409269829928628730747620468964025986524982473540016981249105600555721...

%t Join[{0, 0}, RealDigits[15/16 - Pi*Coth[Pi]/8 + Pi*(Sin[Sqrt[2]*Pi] + Sinh[Sqrt[2]*Pi]) / (4*Sqrt[2]*(Cos[Sqrt[2]*Pi] - Cosh[Sqrt[2]*Pi])), 10, 100][[1]]]

%Y Cf. A024006, A256919, A339529.

%K nonn,cons

%O 0,3

%A _Vaclav Kotesovec_, Dec 08 2020, following a suggestion of _Artur Jasinski_