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A215722
Decimal expansion of Pi*(3 - gamma)/32, where gamma is Euler's constant A001620.
1
2, 3, 7, 8, 5, 6, 2, 9, 5, 8, 8, 6, 8, 0, 5, 5, 0, 6, 7, 4, 2, 9, 6, 2, 3, 6, 3, 0, 8, 0, 2, 3, 3, 3, 9, 4, 7, 9, 6, 3, 7, 0, 1, 2, 5, 5, 2, 3, 5, 2, 2, 3, 9, 5, 4, 4, 6, 5, 2, 1, 4, 2, 8, 0, 8, 5, 1, 8, 5, 6, 2, 4, 6, 6, 3, 3, 9, 3, 2, 7, 9, 9, 1, 3, 7, 1, 1, 2, 1, 7, 8, 7, 9, 8, 3, 7, 5, 2, 3, 8, 3, 7, 7, 2, 9, 5, 5, 5, 3, 4, 0, 9
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
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
Sequence in context: A199966 A011027 A100072 * A324777 A244162 A182516
KEYWORD
nonn,cons,changed
AUTHOR
STATUS
approved