cp's OEIS Frontend

A339083 Decimal expansion of Sum_{k>=0} (zeta(4*k+2)-1).

%I A339083 #32 Jun 06 2024 09:00:29
%S A339083 6,6,3,3,3,7,0,2,3,7,3,4,2,9,0,5,8,7,0,6,7,0,2,5,3,9,7,3,7,5,0,0,0,2,
%T A339083 4,5,2,2,2,8,2,8,1,3,3,2,0,1,9,0,8,3,3,2,7,8,7,5,3,1,2,4,2,1,9,5,0,7,
%U A339083 7,1,2,3,9,5,9,1,5,5,0,1,0,8,7,1,7,8,2,7,7,5,8,7,9,6,9,7,7,4,5,9,3,8,2,5,8,9,4,5
%N A339083 Decimal expansion of Sum_{k>=0} (zeta(4*k+2)-1).
%C A339083 Sum_{k>=1} zeta(4*k)-1 see A256919.
%C A339083 Sum_{k>=1} zeta(4*k+1)-1 see A339097.
%C A339083 Sum_{k>=0} zeta(4*k+3)-1 see A338858.
%C A339083 For additional comments and generalization see A339604.
%F A339083 Equals Sum_{k>=2} k^2/(k^4-1).
%F A339083 Equals -1/8 + Pi*coth(Pi)/4 = -1/8 + A338815 = 3/4 - A256919.
%e A339083 0.663337023734290587067025397375...
%t A339083 RealDigits[N[Sum[Zeta[4 n + 2] - 1, {n, 0, Infinity}], 105]][[1]]
%o A339083 (PARI) suminf(k=0, zeta(4*k+2)-1) \\ _Michel Marcus_, Dec 24 2020
%Y A339083 Cf. A024006, A256919, A338815, A338858, A339097, A339135, A339529, A339530, A339604, A339605, A339605.
%K A339083 nonn,cons
%O A339083 0,1
%A A339083 _Artur Jasinski_, Dec 24 2020
%E A339083 a(104) corrected and more terms from _Georg Fischer_, Jun 06 2024