A243377 - OEIS

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

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

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

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

%N Decimal expansion of a constant related to the asymptotic evaluation of Product_{p prime congruent to 1 modulo 4} (1 + 1/p).

%D Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 2.3 Landau-Ramanujan constant, p. 101.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Landau-RamanujanConstant.html">Ramanujan constant</a>.

%F Equals (4/Pi^(3/2))*exp(gamma/2)*K, where gamma is the Euler-Mascheroni constant and K the Landau-Ramanujan constant.

%F Equals 2/(Pi*A088541) = A060294/A088541. - _Amiram Eldar_, Nov 16 2021

%e 0.732649819283832613620305823117683687363...

%t digits = 103; 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]; 4/Pi^(3/2)*Exp[EulerGamma/2]*LandauRamanujanK // RealDigits[#, 10, digits] & // First (* updated Mar 14 2018 *)

%Y Cf. A001620, A060294, A064533, A088541.

%K nonn,cons,changed

%O 0,1

%A _Jean-François Alcover_, Jun 04 2014