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A299615
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Decimal expansion of W(1) + W(2), where w is the Lambert W function (or PowerLog); see Comments.
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3
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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, 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, 6, 0, 8, 5, 8, 7, 6, 0, 9, 4, 7, 6, 1, 1, 5, 8, 9, 7
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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(2) = W(2/W(1) + 2/W(2)) = log(2) - log(W(1)) - log(W(2)) 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(2) = 1.41974879242350936434644...
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MATHEMATICA
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w[x_] := ProductLog[x]; x = 1; y = 2; u = N[w[x] + w[y], 100]
RealDigits[u, 10][[1]] (* A299615 *)
RealDigits[LambertW[1] + LambertW[2], 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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