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 A088541 Decimal expansion of sqrt(Pi)/(2K)*exp(-gamma/2) where K is the Landau-Ramanujan constant and gamma the Euler-Mascheroni constant. 3
 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 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS An illustration of the Chebyshev effect. REFERENCES S. R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, p. 100 LINKS S. Uchiyama, On some products involving primes, Proc. Amer. Math. Soc. 28 (1971) 629-630; MR 43#3227. FORMULA 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. Equals A002161*A064533/(2*exp(A155739)). - Michel Marcus, Jun 19 2020 EXAMPLE 0.868927768234323... MATHEMATICA 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 *) CROSSREFS Cf. A002161, A064533, A088540, A155739. Sequence in context: A191909 A247559 A246768 * A110214 A305709 A093721 Adjacent sequences: A088538 A088539 A088540 * A088542 A088543 A088544 KEYWORD cons,nonn AUTHOR Benoit Cloitre, Nov 16 2003 STATUS approved

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Last modified January 30 09:15 EST 2023. Contains 359944 sequences. (Running on oeis4.)