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 A299628 #17 Nov 24 2024 20:50:45 %S A299628 5,1,5,2,5,5,3,0,6,0,9,9,4,7,3,4,0,8,5,6,5,8,3,2,4,0,3,2,5,2,1,9,5,5, %T A299628 8,1,8,1,9,3,8,5,2,9,5,0,0,6,4,0,8,9,8,3,0,6,7,9,0,2,2,8,8,1,3,2,6,3, %U A299628 8,2,5,8,5,5,0,4,0,8,7,4,4,9,1,9,2,7 %N A299628 Decimal expansion of 2*W(1/3), where W is the Lambert W function (or PowerLog); see Comments. %C A299628 The Lambert W function satisfies the functional equations %C A299628 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(1/3) = W(2/(9*W(1/3))) = -2*log(3) - 2*log(W(1/3)). See A299613 for a guide to related sequences. %H A299628 G. C. Greubel, <a href="/A299628/b299628.txt">Table of n, a(n) for n = 0..10000</a> %H A299628 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>. %e A299628 2*W(1/3) = 0.5152553060994734085658324032521955... %t A299628 w[x_] := ProductLog[x]; x = 1/3; y = 1/3; u = N[w[x] + w[y], 100] %t A299628 RealDigits[u, 10][[1]] (* A299628 *) %t A299628 RealDigits[2*LambertW[1/3], 10, 100][[1]] (* _G. C. Greubel_, Mar 06 2018 *) %o A299628 (PARI) 2*lambertw(1/3) \\ _G. C. Greubel_, Mar 06 2018 %Y A299628 Cf. A299613, A299629. %K A299628 nonn,cons,easy %O A299628 0,1 %A A299628 _Clark Kimberling_, Mar 03 2018