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 A299622 #18 Nov 24 2024 08:24:53 %S A299622 9,1,8,8,7,7,0,0,1,6,5,8,9,7,9,6,9,9,0,2,4,8,7,7,9,6,3,1,4,0,3,0,6,6, %T A299622 1,4,9,2,5,2,8,0,0,0,2,7,0,3,6,2,4,3,1,2,1,8,1,7,7,4,9,2,5,3,3,3,0,0, %U A299622 6,4,0,3,8,0,7,0,2,3,2,7,7,5,9,0,0,5 %N A299622 Decimal expansion of W(1) + W(1/2), where W is the Lambert W function (or PowerLog); see Comments. %C A299622 The Lambert W function satisfies the functional equations %C A299622 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 W(1) + W(1/2) = W((1/2)*(1/W(1) + 1/W(1/2))) = -log(2) - log(W(1)) - log(W(1/2)). See A299613 for a guide to related sequences. %H A299622 G. C. Greubel, <a href="/A299622/b299622.txt">Table of n, a(n) for n = 0..10000</a> %H A299622 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>. %e A299622 W(1) + W(1/2) = 0.918877001658979699024877963140306614925280002... %t A299622 w[x_] := ProductLog[x]; x = 1; y = 1/2; u = N[w[x] + w[y], 100] %t A299622 RealDigits[u, 10][[1]] (* A299622 *) %t A299622 RealDigits[LambertW[1] + LambertW[1/2], 10, 100][[1]] (* _G. C. Greubel_, Mar 03 2018 *) %o A299622 (PARI) lambertw(1) + lambertw(1/2) \\ _G. C. Greubel_, Mar 03 2018 %Y A299622 Cf. A299613, A299623. %K A299622 nonn,cons,easy %O A299622 0,1 %A A299622 _Clark Kimberling_, Mar 03 2018