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 A299620 #17 Nov 24 2024 08:24:56 %S A299620 1,6,1,7,0,5,2,1,8,5,3,7,3,8,2,3,8,3,2,9,8,8,6,6,5,7,3,2,7,6,3,2,5,3, %T A299620 4,5,4,3,4,3,2,8,2,7,3,0,8,9,2,8,5,3,9,6,1,0,6,8,0,0,2,6,6,2,5,3,9,6, %U A299620 9,4,8,4,3,5,3,1,1,2,7,5,2,4,5,7,8,8 %N A299620 Decimal expansion of W(1) + W(3), where w is the Lambert W function (or PowerLog); see Comments. %C A299620 The Lambert W function satisfies the functional equations %C A299620 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(3) = W(3/W(1) + 3/W(3)) = log(3) - log(W(1)) - log(W(3)). See A299613 for a guide to related sequences. %H A299620 G. C. Greubel, <a href="/A299620/b299620.txt">Table of n, a(n) for n = 1..10000</a> %H A299620 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>. %e A299620 W(1) + W(3) = 1.6170521853738238329886657327632... %t A299620 w[x_] := ProductLog[x]; x = 1; y = 3; u = N[w[x] + w[y], 100] %t A299620 RealDigits[u, 10][[1]] (* A299620 *) %t A299620 RealDigits[LambertW[1] + LambertW[3], 10, 100][[1]] (* _G. C. Greubel_, Mar 03 2018 *) %o A299620 (PARI) lambertw(1) + lambertw(3) \\ _G. C. Greubel_, Mar 03 2018 %Y A299620 Cf. A299613, A299621. %K A299620 nonn,cons,easy %O A299620 1,2 %A A299620 _Clark Kimberling_, Mar 01 2018