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A243376 Decimal expansion of 2*K/Pi, a constant related to the asymptotic evaluation of the number of positive integers all of whose prime factors are congruent to 3 modulo 4, where K is the Landau-Ramanujan constant.

%I A243376 #17 Feb 16 2025 08:33:22
%S A243376 4,8,6,5,1,9,8,8,8,3,8,5,8,9,0,9,9,7,1,2,7,2,4,5,6,4,0,5,8,6,8,2,3,4,
%T A243376 0,5,5,3,8,1,7,1,9,8,1,7,3,9,5,4,1,2,1,3,6,8,8,1,5,4,5,1,0,8,1,6,2,9,
%U A243376 8,5,5,0,9,3,2,0,7,5,8,1,7,1,4,7,6,0,2,0,2,1,0,3,8,1,0,6,9,3,7,1,2
%N A243376 Decimal expansion of 2*K/Pi, a constant related to the asymptotic evaluation of the number of positive integers all of whose prime factors are congruent to 3 modulo 4, where K is the Landau-Ramanujan constant.
%D A243376 Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 2.3 Landau-Ramanujan constant, p. 100.
%H A243376 Gareth A. Jones and Alexander K. Zvonkin, <a href="https://arxiv.org/abs/2401.00270">A number-theoretic problem concerning pseudo-real Riemann surfaces</a>, arXiv:2401.00270 [math.NT], 2023. See page 5.
%H A243376 Eric Weisstein's MathWorld, <a href="https://mathworld.wolfram.com/Landau-RamanujanConstant.html">Ramanujan constant</a>
%F A243376 2*K/Pi, where K is the Landau-Ramanujan constant (A064533).
%e A243376 0.4865198883858909971272456405868234...
%t A243376 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]; 2*LandauRamanujanK/Pi // RealDigits[#, 10, digits] & // First (* updated Mar 14 2018 *)
%Y A243376 Cf. A064533.
%K A243376 nonn,cons
%O A243376 0,1
%A A243376 _Jean-François Alcover_, Jun 04 2014