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%I #8 Mar 04 2018 04:11:45
%S 1,4,1,9,7,4,8,7,9,2,4,2,3,5,0,9,3,6,4,3,4,6,4,4,1,0,7,6,9,0,5,6,7,3,
%T 0,1,6,6,5,2,2,6,9,0,8,7,3,3,7,9,1,6,0,1,6,9,0,7,2,3,8,4,7,3,8,7,5,5,
%U 6,0,8,5,8,7,6,0,9,4,7,6,1,1,5,8,9,7
%N Decimal expansion of W(1) + W(2), where w is the Lambert W function (or PowerLog); see Comments.
%C The Lambert W function satisfies the functional equations 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(2) = W(2/W(1) + 2/W(2)) = log(2) - log(W(1)) - log(W(2)) See A299613 for a guide to related sequences.
%H G. C. Greubel, <a href="/A299615/b299615.txt">Table of n, a(n) for n = 1..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(2) = 1.41974879242350936434644...
%t w[x_] := ProductLog[x]; x = 1; y = 2; u = N[w[x] + w[y], 100]
%t RealDigits[u, 10][[1]] (* A299615 *)
%t RealDigits[LambertW[1] + LambertW[2], 10, 100][[1]] (* _G. C. Greubel_, Mar 03 2018 *)
%o (PARI) lambertw(1) + lambertw(2) \\ _G. C. Greubel_, Mar 03 2018
%Y Cf. A299613, A299616.
%K nonn,cons,easy
%O 1,2
%A _Clark Kimberling_, Mar 01 2018
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