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%I #8 Mar 04 2018 04:10:14
%S 8,4,5,6,0,7,8,3,3,1,7,0,8,5,7,6,6,8,1,0,9,3,2,7,4,0,1,2,3,3,3,3,5,7,
%T 0,5,1,9,3,2,9,3,2,7,5,8,0,6,2,5,8,2,7,3,5,8,8,3,0,9,1,8,4,7,5,8,0,7,
%U 5,1,6,8,5,4,6,6,3,4,4,6,4,8,8,5,2,6
%N Decimal expansion of W(1) + W(1/e), 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(1/e) = W((1/e)(1/W(1)) + 1/W(1/e))) = - 1 - log(W(1)) - log(W(1/e)). See A299613 for a guide to related sequences.
%H G. C. Greubel, <a href="/A299618/b299618.txt">Table of n, a(n) for n = 0..10000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>
%e W(1) + W(1/e) = 0.845607833170857668109327401233335...
%t w[x_] := ProductLog[x]; x = 1; y = 1/E; u = N[w[x] + w[y], 100]
%t RealDigits[u, 10][[1]] (* A299618 *)
%t RealDigits[LambertW[1] + LambertW[1/E], 10, 100][[1]] (* _G. C. Greubel_, Mar 03 2018 *)
%o (PARI) lambertw(1) + lambertw(exp(-1)) \\ _G. C. Greubel_, Mar 03 2018
%Y Cf. A299613, A299619.
%K nonn,cons,easy
%O 0,1
%A _Clark Kimberling_, Mar 01 2018
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