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 A299623 #9 Feb 16 2025 08:33:53 %S A299623 2,5,0,6,4,7,4,0,4,2,6,6,3,8,9,8,8,9,9,4,7,4,4,8,5,8,1,5,3,1,8,9,4,1, %T A299623 7,1,7,4,9,6,4,0,2,3,4,2,3,3,5,7,4,1,5,8,8,0,8,9,8,9,5,4,2,8,6,6,0,1, %U A299623 8,7,2,3,8,8,2,0,4,3,8,5,6,9,1,6,9,0 %N A299623 Decimal expansion of e^(W(1) + W(1/2)) = (1/2)/(W(1)*W(1/2)), where W is the Lambert W function (or PowerLog); see Comments. %C A299623 The Lambert W function satisfies the functional equation e^(W(x) + W(y)) = x*y/(W(x)*W(y)) for x and y greater than -1/e, so that e^(W(1) + W(1/2)) = (1/2)/(W(1)*W(1/2)). See A299613 for a guide to related constants. %H A299623 G. C. Greubel, <a href="/A299623/b299623.txt">Table of n, a(n) for n = 1..10000</a> %H A299623 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a> %e A299623 e^(W(1) + W(1/2)) = 2.506474042663898899474485815318941717... %t A299623 w[x_] := ProductLog[x]; x = 1; y = 1/2; %t A299623 N[E^(w[x] + w[y]), 130] (* A299623 *) %t A299623 RealDigits[1/(2*LambertW[1]*LambertW[1/2]), 10, 100][[1]] (* _G. C. Greubel_, Mar 03 2018 *) %o A299623 (PARI) 1/(2*lambertw(1)*lambertw(1/2)) \\ _G. C. Greubel_, Mar 03 2018 %Y A299623 Cf. A299613, A299622. %K A299623 nonn,cons,easy %O A299623 1,1 %A A299623 _Clark Kimberling_, Mar 03 2018