This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A243379 #30 Feb 16 2025 08:33:22
%S A243379 8,5,6,1,0,8,9,8,1,7,2,1,8,9,3,4,7,6,9,0,6,0,3,3,0,0,6,1,4,8,0,6,1,1,
%T A243379 7,3,4,8,1,0,7,8,4,2,7,3,8,8,1,7,3,4,9,0,8,6,0,5,1,8,4,0,0,5,8,3,4,3,
%U A243379 0,7,9,6,1,1,1,8,6,3,6,5,8,9,6,2,3,3,8,1,2,9,4,5,1,7,7,7,7,0,9,7,6
%N A243379 Decimal expansion of 1/(2*K^2) = Product_(p prime congruent to 3 modulo 4) (1 - 1/p^2), where K is the Landau-Ramanujan constant.
%C A243379 Equals 1/1.168075586.., where 1.168.. is zeta_(m=4,n=3)(s=2) in the table of Section 3.3 of arxiv:1008.2547. - _R. J. Mathar_, Nov 14 2014
%D A243379 Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 2.3 Landau-Ramanujan constant, p. 101.
%H A243379 Richard J. Mathar, <a href="http://arxiv.org/abs/1008.2547">Table of Dirichlet L-Series and Prime Zeta Modulo Functions for Small Moduli</a>, arXiv:1008.2547 [math.NT], 2010-2015.
%H A243379 Eric Weisstein's MathWorld, <a href="https://mathworld.wolfram.com/Landau-RamanujanConstant.html">Ramanujan constant</a>
%F A243379 1/(2*K^2), where K is the Landau-Ramanujan constant (A064533).
%F A243379 A088539 * A243379 = 8 / Pi^2. - _Vaclav Kotesovec_, Apr 30 2020
%e A243379 0.856108981721893476906033006148061173481...
%t A243379 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]; 1/(2*LandauRamanujanK^2) // RealDigits[#, 10, digits] & // First (* updated Mar 18 2018 *)
%Y A243379 Cf. A002145, A064533, A088539, A243381.
%K A243379 nonn,cons
%O A243379 0,1
%A A243379 _Jean-François Alcover_, Jun 04 2014