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A064533
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Decimal expansion of Landau-Ramanujan constant.
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15
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7, 6, 4, 2, 2, 3, 6, 5, 3, 5, 8, 9, 2, 2, 0, 6, 6, 2, 9, 9, 0, 6, 9, 8, 7, 3, 1, 2, 5, 0, 0, 9, 2, 3, 2, 8, 1, 1, 6, 7, 9, 0, 5, 4, 1, 3, 9, 3, 4, 0, 9, 5, 1, 4, 7, 2, 1, 6, 8, 6, 6, 7, 3, 7, 4, 9, 6, 1, 4, 6, 4, 1, 6, 5, 8, 7, 3, 2, 8, 5, 8, 8, 3, 8, 4, 0, 1, 5, 0, 5, 0, 1, 3, 1, 3, 1, 2, 3, 3, 7, 2, 1, 9, 3, 7, 2, 6, 9, 1, 2, 0, 7, 9, 2, 5, 9, 2, 6, 3, 4, 1, 8, 7, 4, 2, 0, 6, 4, 6, 7, 8, 0, 8, 4, 3, 2, 3, 0, 6, 3, 3, 1, 5, 4, 3, 4, 6, 2, 9, 3, 8, 0, 5, 3, 1, 6, 0, 5, 1, 7, 1, 1, 6, 9, 6, 3, 6, 1, 7, 7, 5, 0, 8, 8, 1, 9, 9, 6, 1, 2, 4, 3, 8, 2, 4, 9, 9, 4, 2, 7, 7, 6, 8, 3, 4, 6, 9, 0, 5, 1, 6, 2, 3, 5, 1, 3, 9, 2, 1, 8, 7, 1, 9, 6, 2, 0, 5, 6, 9, 0, 5, 3, 2, 9, 5, 6, 4, 4, 6, 7, 0, 4
(list; constant; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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REFERENCES
| B. C. Berndt, Ramanujan's notebook part IV, Springer-Verlag, 1994, pp. 52,60-66; MR 95e : 11028
S. R. Finch, Mathematical Constants, Cambridge, 2003, pp. 98-104.
Philippe Flajolet and Ilan Vardi, Zeta function Expansions of Classical constants, Feb. 18, 1996
G. H. Hardy, "Ramanujan, Twelve lectures on subjects suggested by his life and work", Chelsea, 1940, pp. 60-63; MR 21 # 4881
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LINKS
| David E. G. Hare, Table of n, a(n) for n = 0..125078
S. R. Finch, Landau-Ramanujan Constant
S. R. Finch, On a Generalized Fermat-Wiles Equation
Ph. Flajolet and I. Vardi, Zeta function expansions of some classical constants
Xavier Gourdon and Pascal Sebah, Constants and records of computation
David E. G. Hare, 125,079 digits of the Landau-Ramanujan constant
David E. G. Hare, Landau-Ramanujan constant up to 10000 digits
Institute of Physics, Constants - Landau-Ramanujan Constant
S. Plouffe, Landau Ramanujan constant
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics
Robert G. Wilson v, The first 15584 digits of the Landau-Ramanujan constant
Wikipedia, the free encyclopedia, Landau-Ramanujan.
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FORMULA
| Victor Adamchik calculated 5100 digits of the Landau-Ramanujan constant using Mathematica (from Mathematica 4 demos): ! (LandauRamanujan[n_] := With[{K = [LeftCeiling]Log[2, n Log[3, 10]] [RightCeiling]}, N[ (1 / (AT)2 ) ( [Product] + (k = 1 ) % K (( ( ((1 - 2^(-2^k)) ) 4^(2^k) Zeta[2^k] ) / (Zeta[2^k, 1/4] - Zeta[2^k, 3/4] )))^(2^((-k)-1))), n]])
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EXAMPLE
| 0.76422365358922066299069873125009232811679054139340951472168667374...
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MATHEMATICA
| First@ RealDigits@ N[1/Sqrt@2 Product[((1 - 2^(-2^k)) 4^(2^k) Zeta[2^k]/(Zeta[2^k, 1/4] - Zeta[2^k, 3/4]))^(2^(-k - 1)), {k, 8}], 2^8] (* Robert G. Wilson v (rgwv(AT)rgwv.com), Jul 01 2007 *)
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CROSSREFS
| Cf. A125766 = Continued fraction. [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), May 13 2009]
Sequence in context: A105419 A175996 A134982 * A131184 A021933 A154730
Adjacent sequences: A064530 A064531 A064532 * A064534 A064535 A064536
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KEYWORD
| cons,nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Oct 08 2001
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EXTENSIONS
| More references needed! Hardy and Wright? Gruber and Lekkerkerker?
More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Oct 08 2001
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