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%I #8 Aug 05 2024 13:41:46
%S 8,4,8,6,3,3,8,6,7,9,6,4,8,8,3,6,3,2,6,8,4,9,0,0,1,2,0,9,0,4,3,0,4,6,
%T 2,9,6,0,0,1,6,6,4,4,6,8,8,1,7,5,5,1,7,1,6,7,9,6,2,0,3,0,9,0,0,3,6,5,
%U 4,2,2,1,3,7,1,3,0,2,1,2,9,1,8,8,6,6,3,4,8,1,0,1,1,5,3,7,0,2,0,6,3,4,4,3,7
%N Decimal expansion of Sum_{k>=2} (zeta(k)/zeta(2*k) - 1).
%H Michael I. Shamos, <a href="https://citeseerx.ist.psu.edu/pdf/ae33a269baba5e8b1038e719fb3209e8a00abec5">Shamos's catalog of the real numbers</a>, 2011. See p. 637.
%F Equals Sum_{k>=2} mu(k)^2/(k*(k-1)) = Sum_{k>=2} 1/A368249(k).
%F Equals Sum_{k>=1} 1/A072777(k).
%F Equals lim_{m->oo} (1/m) * Sum_{k=1..m} A368251(k).
%e 0.84863386796488363268490012090430462960016644688175...
%p evalf(sum(Zeta(k)/Zeta(2*k) - 1, k = 2 .. infinity), 120);
%o (PARI) sumpos(k=2, zeta(k)/zeta(2*k) - 1)
%Y Cf. A008683, A072777, A368249, A368251.
%K nonn,cons
%O 0,1
%A _Amiram Eldar_, Dec 19 2023