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A221710 Decimal expansion of the integral of the logarithm of the Riemann zeta function from 2 to infinity. 0
5, 3, 6, 5, 2, 6, 9, 4, 5, 9, 2, 1, 1, 7, 7, 1, 0, 0, 9, 6, 1, 7, 1, 9, 0, 1, 9, 5, 4, 8, 7, 9, 4, 4, 0, 0, 6, 6, 7, 0, 0, 4, 7, 2, 8, 7, 5, 5, 0, 2, 6, 3, 6, 4, 7, 7, 3, 7, 6, 3, 9, 0, 9, 9, 9, 5, 6, 6, 2, 7, 7, 3, 6, 1, 3, 1, 0, 9, 6, 9, 9, 0, 0, 0, 3, 7, 6, 3, 5, 0, 4, 4, 3, 3, 5, 1, 6, 0, 2, 4 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Table of n, a(n) for n=0..99.

H. Cohen, High-precision calculation of Hardy-Littlewood constants, 1998, see I(2).

R. J. Mathar, Twenty digits of some integrals of the Prime Zeta Function, arXiv:0811.4739, Section 2.4.

EXAMPLE

Integral_{s=2..infinity} log zeta(s) ds = 0.536526945921177100961719019548794400667....

MATHEMATICA

NIntegrate[ Log[ Zeta[s]], {s, 2, Infinity}, WorkingPrecision -> 110] // RealDigits[#, 10, 100]& // First (* Jean-François Alcover, Jun 10 2013 *)

PROG

(PARI) intnum(s=2, [oo, log(2)], log(zeta(s))) \\ Charles R Greathouse IV, Dec 12 2013

CROSSREFS

Cf. A188157.

Sequence in context: A089250 A155681 A075264 * A011504 A237656 A097907

Adjacent sequences:  A221707 A221708 A221709 * A221711 A221712 A221713

KEYWORD

nonn,cons

AUTHOR

N. J. A. Sloane, Jan 26 2013

EXTENSIONS

More digits from Jean-François Alcover, Jun 10 2013

STATUS

approved

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Last modified January 21 11:50 EST 2019. Contains 319355 sequences. (Running on oeis4.)