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 A378131 #8 Nov 19 2024 00:53:55
%S A378131 1,0,1,1,2,0,4,6,9,5,5,3,7,6,9,0,0,9,0,5,7,2,8,5,5,9,8,8,5,6,9,6,2,5,
%T A378131 8,0,3,2,8,3,5,3,6,6,5,8,4,7,9,5,8,1,9,2,0,4,2,2,3,1,0,8,1,0,3,5,4,7,
%U A378131 3,8,0,6,8,3,0,1,1,5,6,1,0,6,0,4,5,1,2,1,7,7
%N A378131 Decimal expansion of sqrt(1 + sqrt(3))*L/(Pi*12^(1/8)), where L is the lemniscate constant (A062539).
%H A378131 Wikipedia, <a href="https://en.wikipedia.org/wiki/Lemniscate_constant">Lemniscate constant</a> (includes this constant).
%H A378131 <a href="/index/Ga#gamma_function">Index to sequences related to the Gamma function</a>.
%F A378131 Equals sqrt((1 + sqrt(3))*Pi)/(2^(3/4)*3^(1/8)*Gamma(3/4)^2) = sqrt(A090388*A000796)/(2^(3/4)*3^(1/8)*A068465^2).
%F A378131 Equals Sum_{j,k integers} exp(-2*Pi*(j^2 + j*k + k^2)).
%F A378131 Equals 2F1(1/3, 2/3, 1, (3*sqrt(3) - 5)/4), where 2F1 is the ordinary hypergeometric function.
%e A378131 1.011204695537690090572855988569625803283536658...
%t A378131 First[RealDigits[Sqrt[(1 + Sqrt[3])*Pi]/(2^(3/4)*3^(1/8)*Gamma[3/4]^2), 10, 100]] (* or *)
%t A378131 First[RealDigits[Hypergeometric2F1[1/3, 2/3, 1, (3*Sqrt[3] - 5)/4], 10, 100]]
%Y A378131 Cf. A000796, A062539, A068465, A090388.
%Y A378131 Cf. A377999, A378128, A378129, A378130, A378132.
%K A378131 nonn,cons,easy
%O A378131 1,5
%A A378131 _Paolo Xausa_, Nov 18 2024