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A299628
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Decimal expansion of 2*W(1/3), where W is the Lambert W function (or PowerLog); see Comments.
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3
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5, 1, 5, 2, 5, 5, 3, 0, 6, 0, 9, 9, 4, 7, 3, 4, 0, 8, 5, 6, 5, 8, 3, 2, 4, 0, 3, 2, 5, 2, 1, 9, 5, 5, 8, 1, 8, 1, 9, 3, 8, 5, 2, 9, 5, 0, 0, 6, 4, 0, 8, 9, 8, 3, 0, 6, 7, 9, 0, 2, 2, 8, 8, 1, 3, 2, 6, 3, 8, 2, 5, 8, 5, 5, 0, 4, 0, 8, 7, 4, 4, 9, 1, 9, 2, 7
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OFFSET
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0,1
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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 2*W(1/3) = W(2)/(9*W(1/3)) = -2*log(3) - 2*log(W(1/3)). See A299613 for a guide to related sequences.
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LINKS
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EXAMPLE
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2*W(1/3) = 0.5152553060994734085658324032521955...
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MATHEMATICA
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w[x_] := ProductLog[x]; x = 1/3; y = 1/3; u = N[w[x] + w[y], 100]
RealDigits[u, 10][[1]] (* A299628 *)
RealDigits[2*LambertW[1/3], 10, 100][[1]] (* G. C. Greubel, Mar 06 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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