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A074760
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Decimal expansion of -B =(1/2)*sum(r in Z, 1/r/(1-r)) where Z is the set of zeros of the Riemann zeta-function which lie in the strip 0 <=Re(z)<=1.
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9
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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
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0,2
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REFERENCES
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H. M. Edwards, Riemann's Zeta Function, Dover Publications Inc. 1974, p. 160.
S. J. Patterson, "An introduction to the theory of the Riemann Zeta-function", Cambridge studies in advanced mathematics 14, p. 34
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LINKS
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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), 37-40; 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.
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FORMULA
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-B = Gamma/2 + 1 - log(4*Pi)/2 = 0.0230957...
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EXAMPLE
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0.023095708966121033814310247906495291621932127152050759525392...
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MATHEMATICA
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RealDigits[ N[ EulerGamma/2 + 1 - Log[4*Pi]/2, 100]] [[1]]
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PROG
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(PARI) Euler/2+1-log(4*Pi)/2 \\ Charles R Greathouse IV, Jan 26 2012
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CROSSREFS
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Cf. A002410 (nearest integer to imaginary part of n-th zeta zero), A195423 (twice the constant).
Sequence in context: A276994 A020823 A021437 * A137914 A098989 A175315
Adjacent sequences: A074757 A074758 A074759 * A074761 A074762 A074763
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KEYWORD
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cons,nonn
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AUTHOR
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Benoit Cloitre, Sep 28 2002
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STATUS
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approved
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