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A243380
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Decimal expansion of 192*K^2*G/Pi^4 = Product_{p prime congruent to 1 modulo 4} (1 + 1/p^2), where K is the Landau-Ramanujan constant and G Catalan's constant.
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11
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1, 0, 5, 4, 4, 3, 9, 9, 4, 4, 7, 9, 9, 9, 4, 8, 4, 8, 9, 6, 4, 8, 8, 1, 9, 4, 6, 4, 8, 2, 6, 7, 1, 7, 9, 4, 8, 3, 1, 7, 3, 4, 3, 6, 5, 0, 6, 9, 7, 0, 6, 0, 4, 8, 8, 0, 7, 8, 4, 8, 9, 7, 2, 7, 6, 1, 8, 5, 7, 7, 4, 6, 8, 0, 4, 2, 1, 5, 8, 2, 9, 3, 8, 7, 1, 6, 4, 3, 3, 6, 0, 3, 3, 7, 6, 6, 8, 5, 7, 0, 9
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OFFSET
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1,3
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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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192*K^2*G/Pi^4, where K is the Landau-Ramanujan constant (A064533) and G Catalan's constant (A006752).
Equals A175647 / 1.001652229636651... both constants from p 26 of arXiv:1008.2537v2. - R. J. Mathar, Aug 21 2022
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EXAMPLE
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1.0544399447999484896488194648267179483...
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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]; 192*LandauRamanujanK^2*Catalan/Pi^4 // RealDigits[#, 10, digits] & // First (* updated Mar 14 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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