A215722 Decimal expansion of Pi*(3 - gamma)/32, where gamma is Euler's constant A001620.

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

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

Sequence in context: A199966 A011027 A100072 * A324777 A244162 A182516

Adjacent sequences: A215719 A215720 A215721 * A215723 A215724 A215725

Keyword

nonn,cons

Author

Charles R Greathouse IV, Aug 22 2012

Status

approved