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A088541
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Decimal expansion of sqrt(Pi)/(2K)*exp(-gamma/2) where K is the Landau-Ramanujan constant and gamma the Euler-Mascheroni constant.
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3
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8, 6, 8, 9, 2, 7, 7, 6, 8, 2, 3, 4, 3, 2, 3, 8, 2, 9, 9, 0, 9, 1, 5, 2, 7, 7, 9, 1, 0, 4, 6, 5, 2, 9, 1, 2, 2, 9, 3, 9, 4, 1, 2, 8, 7, 6, 2, 2, 7, 4, 9, 2, 1, 7, 7, 4, 9, 1, 0, 1, 1, 6, 0, 2, 6, 9, 5, 4, 1, 9, 6, 6, 3, 5, 7, 4, 9, 8, 1, 2, 3, 7, 9, 7, 7, 3, 2, 5, 3, 6, 8, 6, 4, 1, 8, 0, 6, 3, 1, 7, 7, 2, 2, 4
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OFFSET
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0,1
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COMMENTS
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An illustration of the Chebyshev effect.
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REFERENCES
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S. R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, p. 100
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LINKS
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FORMULA
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sqrt(Pi)/(2K)*exp(-gamma/2) = lim x-->oo prod(1-1/p) where p runs through the primes p==3 mod 4 and p<=x.
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EXAMPLE
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0.868927768234323...
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MATHEMATICA
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digits = 104; 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]; Sqrt[Pi]/(2*LandauRamanujanK )*Exp[-EulerGamma/2] // RealDigits[#, 10, digits]& // First (* Jean-François Alcover, Mar 04 2013, 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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