OFFSET
1,2
FORMULA
Equals 1/2 + (coth(Pi) + (sinh(Pi) + sqrt(3)*sin(sqrt(3)*Pi)) / (cosh(Pi) - cos(sqrt(3)*Pi)))*Pi/6.
Equal 3/2 + Sum_{k>=1} (-1)^(k+1) * (zeta(6*k)-1). - Amiram Eldar, May 20 2022
EXAMPLE
1.517100734033216426152907644902413858062211322529844672847634899037901...
MAPLE
evalf(1/2 + (coth(Pi) + (sinh(Pi) + sqrt(3)*sin(sqrt(3)*Pi)) / (cosh(Pi) - cos(sqrt(3)*Pi)))*Pi/6, 100);
MATHEMATICA
RealDigits[Chop[N[Sum[1/(k^6 + 1), {k, 0, Infinity}], 105]]][[1]]
PROG
(PARI) sumpos(k=0, 1/(k^6 + 1))
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Vaclav Kotesovec, May 16 2022
STATUS
approved