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 A299626 #19 Nov 24 2024 08:24:47 %S A299626 2,0,9,9,8,1,7,7,8,9,9,2,8,0,7,9,9,1,9,9,7,7,3,9,4,1,4,1,1,0,5,7,9,5, %T A299626 8,0,9,1,7,8,9,3,3,8,8,7,4,1,2,6,8,2,9,0,5,8,6,5,7,4,3,1,6,6,6,3,3,2, %U A299626 9,8,1,0,0,8,8,8,8,8,5,9,1,5,7,7,1,3 %N A299626 Decimal expansion of 2*W(3), where W is the Lambert W function (or PowerLog); see Comments. %C A299626 The Lambert W function satisfies the functional equations %C A299626 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(3) = W(18/W(3)) = 2*(log(3) - log(W(3))). See A299613 for a guide to related sequences. %H A299626 G. C. Greubel, <a href="/A299626/b299626.txt">Table of n, a(n) for n = 0..10000</a> %H A299626 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>. %e A299626 2*W(3) = 2.0998177899280799199773941411... %t A299626 w[x_] := ProductLog[x]; x = 3; y = 3; u = N[w[x] + w[y], 100] %t A299626 RealDigits[u, 10][[1]] (* A299626 *) %t A299626 RealDigits[2*LambertW[3], 10,100][[1]] (* _G. C. Greubel_, Mar 03 2018 *) %o A299626 (PARI) 2*lambertw(3) \\ _G. C. Greubel_, Mar 03 2018 %Y A299626 Cf. A299613, A299627. %K A299626 nonn,cons,easy %O A299626 0,1 %A A299626 _Clark Kimberling_, Mar 03 2018