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 A299624 #15 Nov 24 2024 08:24:50 %S A299624 1,7,0,5,2,1,1,0,0,4,0,2,7,4,5,0,9,8,2,6,9,2,9,4,4,8,2,9,3,9,0,6,3,4, %T A299624 9,3,3,7,9,6,9,0,6,6,0,0,3,0,2,8,0,7,0,1,7,5,4,4,2,1,4,7,8,9,3,0,5,0, %U A299624 3,0,1,3,1,3,4,8,5,2,6,0,8,9,7,9,3,1 %N A299624 Decimal expansion of 2*W(2), where W is the Lambert W function (or PowerLog); see Comments. %C A299624 The Lambert W function satisfies the functional equations %C A299624 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(2) = W(8/W(2)) = 2*(log(2) - log(W(2))). See A299613 for a guide to related sequences. %H A299624 G. C. Greubel, <a href="/A299624/b299624.txt">Table of n, a(n) for n = 0..10000</a> %H A299624 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>. %e A299624 2*W(2) = 1.7052110040274509826929448293906349337... %t A299624 w[x_] := ProductLog[x]; x = 2; y = 2; u = N[w[x] + w[y], 100] %t A299624 RealDigits[u, 10][[1]] (* A299624 *) %t A299624 RealDigits[2*LambertW[2],10,100][[1]] (* _G. C. Greubel_, Mar 03 2018 *) %o A299624 (PARI) 2*lambertw(2) \\ _G. C. Greubel_, Mar 03 2018 %Y A299624 Cf. A299613, A299625. %K A299624 nonn,cons,easy %O A299624 0,2 %A A299624 _Clark Kimberling_, Mar 03 2018