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A354052
Decimal expansion of Sum_{k>=0} 1 / (k^6 + 1).
3
1, 5, 1, 7, 1, 0, 0, 7, 3, 4, 0, 3, 3, 2, 1, 6, 4, 2, 6, 1, 5, 2, 9, 0, 7, 6, 4, 4, 9, 0, 2, 4, 1, 3, 8, 5, 8, 0, 6, 2, 2, 1, 1, 3, 2, 2, 5, 2, 9, 8, 4, 4, 6, 7, 2, 8, 4, 7, 6, 3, 4, 8, 9, 9, 0, 3, 7, 9, 0, 1, 3, 5, 0, 5, 3, 5, 7, 9, 8, 7, 2, 0, 0, 7, 8, 4, 3, 6, 9, 3, 6, 9, 3, 3, 0, 0, 6, 4, 3, 7, 0, 6, 6, 6, 4
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