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