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A202350
Decimal expansion of x > 0 satisfying e*x + 1 = exp(x).
2
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
OFFSET
1,2
COMMENTS
See A202320 for a guide to related sequences. The Mathematica program includes a graph.
LINKS
FORMULA
Equals -LambertW(-1, -1/exp(1+1/e)) - 1/e. - Andrea Pinos, Sep 12 2023
EXAMPLE
x = 1.750786722680146367570014877255332...
MATHEMATICA
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]
RealDigits[r] (* A202350 *)
(* alternate program *)
RealDigits[(-1 - E*ProductLog[-1, -E^(-1-1/E)])/E, 10, 99] // First (* Jean-François Alcover, Feb 27 2013 *)
CROSSREFS
Sequence in context: A184908 A197519 A290374 * A096435 A021855 A350544
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Dec 17 2011
STATUS
approved