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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 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

See A202320 for a guide to related sequences. The Mathematica program includes a graph.

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..10000

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: A151689 A216833 A242046 * A266120 A296348 A088438

Adjacent sequences:  A202344 A202345 A202346 * A202348 A202349 A202350

KEYWORD

nonn,cons

AUTHOR

Clark Kimberling, Dec 17 2011

STATUS

approved

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Last modified June 15 17:43 EDT 2019. Contains 324142 sequences. (Running on oeis4.)