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%I #11 Mar 14 2018 10:37:14
%S 3,2,7,1,2,9,3,6,6,9,4,1,0,2,6,3,8,2,4,0,0,2,3,2,8,6,9,0,2,8,3,9,2,7,
%T 9,9,6,9,5,0,4,7,5,4,0,9,6,1,3,0,3,4,8,6,9,1,6,7,8,1,1,1,1,5,7,8,9,0,
%U 5,1,5,3,4,6,1,6,5,7,3,8,9,9,6,8,2,5,1,4,4,1,4,5,4,0,9,8,6,8,0,3,2,8,3,8
%N Decimal expansion of 1/(4*K), a constant related to the asymptotic evaluation of the number of positive integers all of whose prime factors are congruent to 1 modulo 4, where K is the Landau-Ramanujan constant.
%D Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 2.3 Landau-Ramanujan constant, p. 100.
%H Eric Weisstein's MathWorld, <a href="http://mathworld.wolfram.com/Landau-RamanujanConstant.html">Ramanujan constant</a>
%F 1/(4*K), where K is the Landau-Ramanujan constant.
%e 0.327129366941026382400232869028392799695...
%t 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]; 1/(4*LandauRamanujanK) // RealDigits[#, 10, digits] & // First (* updated Mar 18 2018 *)
%Y Cf. A064533.
%K nonn,cons
%O 0,1
%A _Jean-François Alcover_, Jun 04 2014