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A299620
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Decimal expansion of W(1) + W(3), where w is the Lambert W function (or PowerLog); see Comments.
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3
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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, 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, 9, 4, 8, 4, 3, 5, 3, 1, 1, 2, 7, 5, 2, 4, 5, 7, 8, 8
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OFFSET
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1,2
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COMMENTS
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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(3) = W(W(3/W(1)) + 3/W(3)) = log(3) - log(W(1)) - log(W(3)). See A299613 for a guide to related sequences.
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LINKS
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EXAMPLE
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W(1) + W(3) = 1.6170521853738238329886657327632...
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MATHEMATICA
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w[x_] := ProductLog[x]; x = 1; y = 3; u = N[w[x] + w[y], 100]
RealDigits[u, 10][[1]] (* A299620 *)
RealDigits[LambertW[1] + LambertW[3], 10, 100][[1]] (* G. C. Greubel, Mar 03 2018 *)
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PROG
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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