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A234015 K' (K being A105459) = Sum_{k>=0} (Zeta(k+1/2)-1)/(2k+1), negated.

%I A234015 #18 Jun 17 2021 09:33:27
%S A234015 1,8,2,6,5,0,7,8,1,0,8,5,8,4,7,8,5,5,8,8,1,5,7,6,5,4,0,6,1,3,0,3,2,1,
%T A234015 9,7,3,0,9,9,4,9,1,4,8,4,9,4,3,4,9,0,6,6,8,3,2,2,9,0,1,3,6,3,7,7,6,4,
%U A234015 9,9,2,7,1,8,3,8,7,3,5,8,4,6,4,7,9,7,3,1,3,6,2,1,5,8,3,2,8,9,9,4,2,0,4,7,1
%N A234015 K' (K being A105459) = Sum_{k>=0} (Zeta(k+1/2)-1)/(2k+1), negated.
%H A234015 David Brink, <a href="http://www.jstor.org/stable/10.4169/amer.math.monthly.119.09.779">The Spiral of Theodorus and Sums of Zeta-values at the Half-Integers</a>, The American Mathematical Monthly, Vol. 119, No. 9 (November 2012), page 785.
%H A234015 Steven R. Finch, <a href="https://doi.org/10.1017/9781316997741">Mathematical Constants II</a>, Encyclopedia of Mathematics and Its Applications, Cambridge University Press, Cambridge, 2018, p. 663 (constant K').
%e A234015 1.8265078108584785588157654061303219730994914849434906683229013637764992...
%t A234015 RealDigits[ Sum[ (Zeta[k + 1/2] - 1)/(2 k + 1), {k, 0, 370}], 10,  111][[1]]
%o A234015 (PARI) sum(k=0,340,(zeta(k+1/2)-1)/(2*k+1))
%Y A234015 Cf. A105459, A226317, A234014.
%K A234015 nonn,easy,cons
%O A234015 1,2
%A A234015 _David Brink_ and _Robert G. Wilson v_, Dec 18 2013