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A299629
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Decimal expansion of e^(2*W(1/3)) = (1/9)/(W(1/3))^2, where W is the Lambert W function (or PowerLog); see Comments.
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3
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1, 6, 7, 4, 0, 6, 5, 8, 4, 6, 4, 6, 4, 8, 8, 0, 7, 7, 2, 2, 2, 6, 0, 8, 1, 1, 1, 4, 3, 8, 9, 3, 4, 0, 0, 8, 4, 2, 0, 3, 5, 4, 5, 3, 3, 0, 1, 6, 1, 8, 2, 3, 2, 7, 2, 3, 3, 7, 9, 1, 8, 0, 6, 1, 4, 3, 4, 5, 8, 5, 5, 2, 5, 5, 5, 1, 9, 6, 8, 1, 3, 2, 8, 1, 6, 2
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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 equation e^(W(x) + W(y)) = x*y/(W(x)*W(y)) for x and y greater than -1/e, so that e^(2*W(1/3)) = (1/9)/(W(1/3))^2. See A299613 for a guide to related constants.
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LINKS
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EXAMPLE
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e^(2*W(1/3)) = 1.674065846464880772226081114...
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MATHEMATICA
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w[x_] := ProductLog[x]; x = 1/3; y = 1/3; N[E^(w[x] + w[y]), 130] (* A299629 *)
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PROG
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(PARI) exp(2*lambertw(1/3)) \\ Altug Alkan, Mar 13 2018
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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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