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 A242013 #45 Jun 16 2025 08:58:01
%S A242013 1,6,3,8,9,7,3,1,8,6,3,4,5,8,1,5,9,5,8,5,6,2,9,9,7,6,9,0,0,4,7,3,5,1,
%T A242013 1,8,6,0,9,6,6,5,7,4,6,1,4,3,5,4,5,0,4,3,6,4,6,8,4,2,5,9,8,5,3,0,5,0,
%U A242013 2,4,6,3,1,1,1,9,0,0,6,9,2,2,8,6,0,2,4,7,2,2,6,2,9,8,4,8,2,6,9,9,2
%N A242013 Decimal expansion of the Euler-Kronecker constant (as named by P. Moree) for hypotenuse numbers.
%C A242013 130000 digits are available (see Links). - _Alessandro Languasco_, Mar 27 2024
%D A242013 Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 2.3 Landau-Ramanujan constants, p. 99.
%H A242013 Steven R. Finch, <a href="http://arxiv.org/abs/2001.00578">Errata and Addenda to Mathematical Constants</a>, arXiv:2001.00578 [math.HO], 202-2024, p. 11.
%H A242013 Alessandro Languasco, <a href="https://www.dei.unipd.it/~languasco/CLM.html">Programs and numerical results for the paper "Landau and Ramanujan approximations for divisor sums and coefficients of cusp forms"</a>.
%H A242013 Alessandro Languasco, <a href="https://doi.org/10.24433/CO.9485449.v2">Shanks' asymptotic constants for the number of positive integers less or equal than x that are the sum of two squares (Source code)</a>, gp script, 2024.
%H A242013 Pieter Moree, <a href="https://arxiv.org/abs/1110.0708">Counting numbers in multiplicative sets: Landau versus Ramanujan</a>, p. 13, arXiv:1110.0708v1 [math.NT] 4 Oct 2011.
%H A242013 D. Shanks, <a href="http://dx.doi.org/10.1090/S0025-5718-1964-0159174-9">The second-order term in the asymptotic expansion of B(x)</a>, Mathematics of Computation 18 (1964), pp. 75-86.
%H A242013 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Landau-RamanujanConstant.html">Landau-Ramanujan Constant</a>.
%F A242013 1 - 2*A227158.
%e A242013 -0.1638973186345815958562997690047351186096657461435450436468425985305...
%t A242013 digits = 101; m0 = 5; dm = 5; beta[x_] := 1/4^x*(Zeta[x, 1/4] - Zeta[x, 3/4]); L = Pi^(3/2)/Gamma[3/4]^2*2^(1/2)/2; Clear[f]; f[m_] := f[m] = 1/2*(1 - Log[Pi*E^EulerGamma/(2*L)]) - 1/4*NSum[Zeta'[2^k]/Zeta[2^k] - beta'[2^k]/beta[2^k] + Log[2]/(2^(2^k) - 1), {k, 1, m}, WorkingPrecision -> digits + 10]; f[m0]; f[m = m0 + dm]; While[RealDigits[f[m], 10, digits] != RealDigits[f[m - dm], 10, digits], m = m + dm]; RealDigits[1 - 2*f[m], 10, digits] // First
%Y A242013 Cf. A227158.
%K A242013 nonn,cons
%O A242013 0,2
%A A242013 _Jean-François Alcover_, Aug 11 2014