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 A340422 #11 Feb 28 2023 23:48:04
%S A340422 2,5,5,1,6,9,8,8,0,6,4,0,3,9,2,4,3,6,0,9,9,3,5,6,1,6,7,8,6,0,5,6,2,9,
%T A340422 3,1,4,3,2,5,4,3,6,9,2,6,5,4,9,2,9,5,7,2,7,5,9,1,2,2,1,3,3,9,3,8,3,5,
%U A340422 1,7,2,0,1,7,5,7,6,9,2,2,8,6,3,6,4,8,1,7,0,5,3,4,6,6,6,6,1,4,2,4,5,7,0,6,0
%N A340422 Decimal expansion of Integral_{x=0..Pi/2, y=0..Pi/2} log(1 + 2*sin(x)^2 + 2*sin(y)^2) dy dx.
%F A340422 Equals Pi * Integral_{x=0..Pi/2} (log(1 + sqrt(1 + 2/(3 - 2*cos(x)^2))) + log((1 + 2*sin(x)^2)/4)/2) dx.
%F A340422 Equals limit_{n->infinity} Pi^2 * log(A067518(n))/(4*n^2) - Pi^2*log(2)/4 - G*Pi, where G is Catalan's constant A006752.
%e A340422 2.551698806403924360993561678605629314325436926549295727591221339383517201757...
%t A340422 RealDigits[N[Pi*Integrate[(Log[1 + Sqrt[1 + 2/(3 - 2*Cos[x]^2)]] + Log[(1 + 2*Sin[x]^2)/4]/2), {x, 0, Pi/2}], 120], 10, 110][[1]]
%Y A340422 Cf. A067518, A340322, A340350, A340421.
%K A340422 nonn,cons
%O A340422 1,1
%A A340422 _Vaclav Kotesovec_, Jan 07 2021