A243372 - OEIS

%I #9 Feb 16 2025 08:33:22

%S 4,9,0,6,9,4,0,5,0,4,1,1,5,3,9,5,7,3,6,0,0,3,4,9,3,0,3,5,4,2,5,8,9,1,

%T 9,9,5,4,2,5,7,1,3,1,1,4,4,1,9,5,5,2,3,0,3,7,5,1,7,1,6,6,7,3,6,8,3,5,

%U 7,7,3,0,1,9,2,4,8,6,0,8,4,9,5,2,3,7,7,1,6,2,1,8,1,1,4,8,0,2,0,4,9,2,5,7

%N Decimal expansion of 3/(8*K), a constant related to the asymptotic evaluation of the number of positive integers that can be expressed as the sum of two coprime squares, 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="https://mathworld.wolfram.com/Landau-RamanujanConstant.html">Ramanujan constant</a>

%F 3/(8*K), where K is the Landau-Ramanujan constant.

%e 0.490694050411539573600349303542589...

%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]; 3/(8*LandauRamanujanK) // RealDigits[#, 10, digits] & // First (* updated Mar 14 2018 *)

%Y Cf. A064533.

%K nonn,cons,changed

%O 0,1

%A _Jean-François Alcover_, Jun 04 2014