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A202347
Decimal expansion of x < 0 satisfying x + e = exp(x).
3
2, 6, 4, 7, 4, 5, 0, 2, 4, 2, 0, 4, 9, 9, 6, 6, 7, 2, 0, 7, 2, 7, 2, 0, 1, 2, 2, 2, 1, 4, 6, 4, 1, 5, 2, 4, 3, 5, 5, 9, 2, 9, 7, 3, 7, 7, 0, 8, 0, 1, 9, 6, 6, 8, 3, 0, 5, 4, 0, 3, 2, 2, 2, 7, 8, 8, 5, 8, 1, 1, 9, 4, 6, 0, 7, 5, 9, 2, 2, 7, 8, 4, 5, 5, 2, 1, 4, 9, 0, 3, 3, 5, 7, 2, 7, 8, 8, 0, 3
OFFSET
1,1
COMMENTS
See A202320 for a guide to related sequences. The Mathematica program includes a graph.
LINKS
FORMULA
Equals -exp(1) - lambertw(-exp(-exp(1)). - G. C. Greubel, Nov 09 2017
EXAMPLE
x < 0: -2.64745024204996672072720122214641524...
x > 0: 1.420370118020083458458421283899772980...
MATHEMATICA
u = 1; v = E;
f[x_] := u*x + v; g[x_] := E^x
Plot[{f[x], g[x]}, {x, -3, 2}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, -2.7, -2.6}, WorkingPrecision -> 110]
RealDigits[r] (* A202347 *)
r = x /. FindRoot[f[x] == g[x], {x, 1.4, 1.5}, WorkingPrecision -> 110]
RealDigits[r] (* A104689 *)
RealDigits[-E - LambertW[-Exp[-E]], 10, 100][[1]] (* G. C. Greubel, Nov 09 2017 *)
PROG
(PARI) solve(x=-3, 0, exp(x)-exp(1)-x) \\ Michel Marcus, Nov 09 2017
CROSSREFS
Cf. A202320.
Sequence in context: A242046 A330776 A327458 * A364897 A266120 A296348
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Dec 17 2011
STATUS
approved