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A074760
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Decimal expansion of lambda(1) in Li's criterion.
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21
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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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COMMENTS
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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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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.
E. Bombieri and J. C. Lagarias, Complements to Li's Criterion for the Riemann Hypothesis, J. Number Th. 77(2) (1999), 274-287.
M. W. Coffey, Relations and positivity results for derivatives of the Riemann xi function, J. Comput. Appl. Math. 166(2) (2004), 525-534.
Xian-Jin Li, The positivity of a sequence of numbers and the Riemann hypothesis, J. Number Th. 65(2) (1997), 325-333.
J. Sondow and C. Dumitrescu, A monotonicity property of Riemann's xi function and a reformulation of the Riemann Hypothesis, arXiv:1005.1104 [math.NT], 2010; see p. 3 in the link.
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. 39 in the link.
Eric Weisstein's World of Mathematics, Li's Criterion.
Eric Weisstein's World of Mathematics, Riemann Zeta Function Zeros.
Wikipedia, Li's criterion.
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[EulerGamma/2 + 1 - Log[4 Pi]/2, 10, 110][[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).
Cf. A104539 (lambda_2), A104540 (lambda_3), A104541 (lambda_4), A104542 (lambda_5).
Cf. A306339 (lambda_6), A306340 (lambda_7), A306341 (lambda_8).
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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EXTENSIONS
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Name simplified by Eric W. Weisstein, Feb 08 2019
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STATUS
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approved
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