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

Author

Charles R Greathouse IV, Aug 22 2012

Keywords

• nonn
• cons

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.

Examples

			0.237856295886805506742962363080233394796370125523522395446521428085...
		

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.

Programs

Magma

R:= RealField(100); Pi(R)*(3 - EulerGamma(R))/32; // G. C. Greubel, Aug 27 2018

Mathematica

RealDigits[Pi*(3 - EulerGamma)/32, 10, 100][[1]] (* G. C. Greubel, Aug 27 2018 *)

PARI

Pi*(3-Euler)/32