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A202350
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Decimal expansion of x > 0 satisfying e*x + 1 = exp(x).
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2
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1, 7, 5, 0, 7, 8, 6, 7, 2, 2, 6, 8, 0, 1, 4, 6, 3, 6, 7, 5, 7, 0, 0, 1, 4, 8, 7, 7, 2, 5, 5, 3, 3, 2, 8, 9, 4, 1, 3, 7, 8, 6, 6, 3, 4, 9, 4, 0, 8, 2, 6, 8, 4, 9, 0, 8, 0, 5, 9, 4, 5, 7, 5, 6, 1, 6, 0, 8, 4, 7, 8, 6, 1, 9, 5, 5, 1, 7, 3, 2, 0, 6, 4, 9, 0, 1, 6, 9, 1, 4, 7, 2, 5, 8, 0, 3, 7, 0, 8
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OFFSET
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1,2
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COMMENTS
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See A202320 for a guide to related sequences. The Mathematica program includes a graph.
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LINKS
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FORMULA
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Equals -LambertW(-1, -1/exp(1+1/e)) - 1/e. - Andrea Pinos, Sep 12 2023
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EXAMPLE
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x = 1.750786722680146367570014877255332...
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MATHEMATICA
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u = E; v = 1;
f[x_] := u*x + v; g[x_] := E^x
Plot[{f[x], g[x]}, {x, -1, 2}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, 1.7, 1.8}, WorkingPrecision -> 110]
(* alternate program *)
RealDigits[(-1 - E*ProductLog[-1, -E^(-1-1/E)])/E, 10, 99] // First (* Jean-François Alcover, Feb 27 2013 *)
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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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