OFFSET
0,1
COMMENTS
Volchkov shows that this is equal to integral(t=0..oo, (1-12*t^2)/(1+4*t^2)^3) * integral(s=1/2..oo, log |zeta(s + i*t)|) if and only if the Riemann hypothesis holds.
REFERENCES
Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 1.6.2, p. 42.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..10000
V. V. Volchkov, On an equality equivalent to the Riemann hypothesis, Ukrainian Mathematical Journal 47:3 (1995), pp. 491-493.
EXAMPLE
0.237856295886805506742962363080233394796370125523522395446521428085...
MATHEMATICA
RealDigits[Pi*(3 - EulerGamma)/32, 10, 100][[1]] (* G. C. Greubel, Aug 27 2018 *)
PROG
(PARI) Pi*(3-Euler)/32
(Magma) R:= RealField(100); Pi(R)*(3 - EulerGamma(R))/32; // G. C. Greubel, Aug 27 2018
CROSSREFS
KEYWORD
AUTHOR
Charles R Greathouse IV, Aug 22 2012
STATUS
approved