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A243379
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Decimal expansion of 1/(2*K^2) = Product_(p prime congruent to 3 modulo 4) (1 - 1/p^2), where K is the Landau-Ramanujan constant.
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14
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8, 5, 6, 1, 0, 8, 9, 8, 1, 7, 2, 1, 8, 9, 3, 4, 7, 6, 9, 0, 6, 0, 3, 3, 0, 0, 6, 1, 4, 8, 0, 6, 1, 1, 7, 3, 4, 8, 1, 0, 7, 8, 4, 2, 7, 3, 8, 8, 1, 7, 3, 4, 9, 0, 8, 6, 0, 5, 1, 8, 4, 0, 0, 5, 8, 3, 4, 3, 0, 7, 9, 6, 1, 1, 1, 8, 6, 3, 6, 5, 8, 9, 6, 2, 3, 3, 8, 1, 2, 9, 4, 5, 1, 7, 7, 7, 7, 0, 9, 7, 6
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OFFSET
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0,1
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COMMENTS
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Equals 1/1.168075586.., where 1.168.. is zeta_(m=4,n=3)(s=2) in the table of Section 3.3 of arxiv:1008.2547. - R. J. Mathar, Nov 14 2014
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REFERENCES
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Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 2.3 Landau-Ramanujan constant, p. 101.
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LINKS
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FORMULA
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1/(2*K^2), where K is the Landau-Ramanujan constant (A064533).
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EXAMPLE
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0.856108981721893476906033006148061173481...
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MATHEMATICA
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digits = 101; LandauRamanujanK = 1/Sqrt[2]*NProduct[((1 - 2^(-2^n))*Zeta[2^n]/DirichletBeta[2^n])^(1/2^(n + 1)), {n, 1, 24}, WorkingPrecision -> digits + 5]; 1/(2*LandauRamanujanK^2) // RealDigits[#, 10, digits] & // First (* updated Mar 18 2018 *)
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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