A234015 K' (K being A105459) = Sum_{k>=0} (Zeta(k+1/2)-1)/(2k+1), negated.
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, 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, 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
Offset: 1
Examples
1.8265078108584785588157654061303219730994914849434906683229013637764992...
Links
- David Brink, The Spiral of Theodorus and Sums of Zeta-values at the Half-Integers, The American Mathematical Monthly, Vol. 119, No. 9 (November 2012), page 785.
- Steven R. Finch, Mathematical Constants II, Encyclopedia of Mathematics and Its Applications, Cambridge University Press, Cambridge, 2018, p. 663 (constant K').
Programs
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Mathematica
RealDigits[ Sum[ (Zeta[k + 1/2] - 1)/(2 k + 1), {k, 0, 370}], 10, 111][[1]] -
PARI
sum(k=0,340,(zeta(k+1/2)-1)/(2*k+1))