A234014 Decimal expansion of Sum_{x>=2} 1/((x - 1) sqrt(x)) = Sum_{k>=1} (zeta(k+1/2) - 1).

2, 1, 8, 4, 0, 0, 9, 4, 7, 0, 2, 6, 7, 8, 5, 1, 9, 5, 2, 8, 9, 4, 7, 3, 4, 1, 5, 7, 8, 5, 2, 9, 4, 9, 0, 7, 0, 4, 4, 3, 9, 0, 8, 4, 0, 6, 2, 6, 3, 2, 2, 9, 4, 2, 0, 2, 0, 0, 2, 5, 1, 2, 0, 7, 9, 2, 8, 3, 5, 4, 9, 0, 3, 1, 1, 2, 7, 4, 0, 2, 9, 5, 3, 9, 0, 6, 9, 7, 4, 1, 8, 4, 6, 1, 3, 4, 1, 6, 1, 9, 7, 2, 3, 0, 7

Offset

1,1

Links

Table of n, a(n) for n=1..105.

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.

Example

2.184009470267851952894734157852949070443908406263229420200251207928354...

Mathematica

RealDigits[ Sum[ Zeta[k + 1/2] - 1, {k, 1, 355}], 10, 111][[1]]

Prog

(PARI) sum(k=1, 340, zeta(k+1/2)-1)

Crossrefs

Cf. A105459, A226317, A234015.

Sequence in context: A085470 A200584 A099379 * A367994 A208931 A133214

Adjacent sequences: A234011 A234012 A234013 * A234015 A234016 A234017

Keyword

nonn,easy,cons

Author

David Brink and Robert G. Wilson v, Dec 18 2013

Status

approved