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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 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Volchkov shows that this is equal to integral(t=0..infinity, (1-12t^2)/(1+4t^2)^3) * integral(s=1/2..infinity, log |zeta(s + it)|) if and only if the Riemann hypothesis holds.

REFERENCES

V. V. Volchkov, On an equality equivalent to the Riemann hypothesis, Ukranian Mathematical Journal 47:3 (1995), pp. 491-493. doi:10.1007/BF01056314

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..10000

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

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Last modified April 5 20:05 EDT 2020. Contains 333260 sequences. (Running on oeis4.)