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 A299632 #9 Nov 24 2024 20:48:44 %S A299632 1,3,7,0,1,5,3,8,8,4,3,0,9,1,8,7,8,9,2,0,5,6,4,9,8,9,6,1,0,7,5,2,6,0, %T A299632 3,7,6,8,2,8,1,1,1,4,3,1,3,6,1,6,4,1,0,6,7,0,8,1,9,6,0,3,0,9,9,7,5,0, %U A299632 0,7,7,5,7,0,2,2,3,7,6,2,9,5,6,2,3,9 %N A299632 Decimal expansion of 2*W(e/2), where W is the Lambert W function (or PowerLog); see Comments. %C A299632 The Lambert W function satisfies the functional equations %C A299632 W(x) + W(y) = W(x*y*(1/W(x) + 1/W(y))) = log(x*y)/(W(x)*W(y)) for x and y greater than -1/e, so that 2*W(e/2) = W(e^2/(2*W(e/2))) = 2 - log(4) - 2*log(W(e/2)). See A299613 for a guide to related sequences. %H A299632 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>. %e A299632 2*W(e/2) = 1.3701538843091878920564989610752603... %t A299632 w[x_] := ProductLog[x]; x = E/2; y = E/2; u = N[w[x] + w[y], 100] %t A299632 RealDigits[u, 10][[1]] (* A299632 *) %o A299632 (PARI) 2*lambertw(exp(1)/2) \\ _Altug Alkan_, Mar 13 2018 %Y A299632 Cf. A299613, A299632. %K A299632 nonn,cons,easy %O A299632 0,2 %A A299632 _Clark Kimberling_, Mar 13 2018