

A074760


Decimal expansion of B =(1/2)*sum(r in Z, 1/r/(1r)) where Z is the set of zeros of the Riemann zetafunction which lie in the strip 0 <=Re(z)<=1.


9



0, 2, 3, 0, 9, 5, 7, 0, 8, 9, 6, 6, 1, 2, 1, 0, 3, 3, 8, 1, 4, 3, 1, 0, 2, 4, 7, 9, 0, 6, 4, 9, 5, 2, 9, 1, 6, 2, 1, 9, 3, 2, 1, 2, 7, 1, 5, 2, 0, 5, 0, 7, 5, 9, 5, 2, 5, 3, 9, 2, 0, 7, 2, 2, 1, 2, 9, 7, 1, 3, 5, 6, 4, 7, 6, 7, 2, 4, 5, 7, 9, 9, 7, 0, 7, 9, 8, 5, 6, 9, 5, 1, 1, 7, 0, 9, 8, 3, 3, 3, 6, 4, 3, 0
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OFFSET

0,2


REFERENCES

H. M. Edwards, Riemann's Zeta Function, Dover Publications Inc. 1974, p. 160.
S. J. Patterson, "An introduction to the theory of the Riemann Zetafunction", Cambridge studies in advanced mathematics 14, p. 34


LINKS

Table of n, a(n) for n=0..103.
J. Sondow and C. Dumitrescu, A monotonicity property of Riemann's xi function and a reformulation of the Riemann Hypothesis, Periodica Math. Hungarica, 60 (2010), 3740; see p. 3 in the link.
Eric Weisstein's World of Mathematics, Li's Criterion
Eric Weisstein's World of Mathematics, Riemann Zeta Function Zeros
Index entries for zeta function.


FORMULA

B = Gamma/2 + 1  log(4*Pi)/2 = 0.0230957...


EXAMPLE

0.023095708966121033814310247906495291621932127152050759525392...


MATHEMATICA

RealDigits[ N[ EulerGamma/2 + 1  Log[4*Pi]/2, 100]] [[1]]


PROG

(PARI) Euler/2+1log(4*Pi)/2 \\ Charles R Greathouse IV, Jan 26 2012


CROSSREFS

Cf. A002410 (nearest integer to imaginary part of nth zeta zero), A195423 (twice the constant).
Sequence in context: A276994 A020823 A021437 * A137914 A098989 A175315
Adjacent sequences: A074757 A074758 A074759 * A074761 A074762 A074763


KEYWORD

cons,nonn


AUTHOR

Benoit Cloitre, Sep 28 2002


STATUS

approved



