A245276 Decimal expansion of sum_{r in Z}(1/r^3) where Z is the set of all nontrivial zeros r of the Riemann zeta function.

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

Offset

0,8

References

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 2.21 Stieltjes Constants, p. 168.

Links

Table of n, a(n) for n=0..105.

Eric Weisstein's MathWorld, Stieltjes Constants

Wikipedia, Stieltjes constants

Formula

-7*zeta(3)/8 + gamma^3 + 3*gamma*gamma(1) + 3/2*gamma(2) + 1, where gamma is Euler's constant and gamma(n) is the n-th Stieltjes constant.

Example

-0.000111158231452105922762668238914578473964189248986518770273452672891213...

Mathematica

Join[{0, 0, 0}, RealDigits[-7*Zeta[3]/8 + EulerGamma^3 + 3*EulerGamma*StieltjesGamma[1] + 3/2*StieltjesGamma[2] + 1, 10, 103] // First]

Crossrefs

Cf. A074760, A195423, A245275.

Sequence in context: A195358 A021636 A011210 * A180155 A110989 A099736

Adjacent sequences: A245273 A245274 A245275 * A245277 A245278 A245279

Keyword

nonn,cons

Author

Jean-François Alcover, Jul 16 2014

Status

approved