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A202324 Decimal expansion of x < 0 satisfying x + 3 = exp(x). 3
2, 9, 4, 7, 5, 3, 0, 9, 0, 2, 5, 4, 2, 2, 8, 5, 1, 2, 7, 5, 9, 0, 1, 2, 6, 3, 8, 8, 7, 1, 3, 9, 8, 1, 6, 4, 1, 4, 4, 5, 8, 0, 0, 7, 6, 4, 5, 3, 9, 9, 6, 8, 9, 0, 4, 8, 9, 6, 6, 1, 8, 2, 8, 6, 6, 9, 1, 5, 6, 3, 9, 3, 7, 8, 3, 2, 2, 1, 1, 0, 0, 2, 3, 9, 5, 4, 7, 7, 7, 6, 5, 5, 4, 3, 8, 9, 1, 5, 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 -3 - LambertW(-exp(-3)). - G. C. Greubel, Nov 09 2017

EXAMPLE

x < 0: -2.9475309025422851275901263887139816414...

x > 0:  1.50524149579288336699862443213735394007...

MATHEMATICA

u = 1; v = 3;

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, -1}, WorkingPrecision -> 110]

RealDigits[r]  (* A202324 *)

r = x /. FindRoot[f[x] == g[x], {x, 1.5, 1.6}, WorkingPrecision -> 110]

RealDigits[r]  (* A202325 *)

RealDigits[-3 - LambertW[-Exp[-3]], 10, 100][[1]] (* G. C. Greubel, Nov 09 2017 *)

PROG

(PARI) solve(x=-3, 0, x+3-exp(x)) \\ Michel Marcus, Nov 09 2017

CROSSREFS

Cf. A202320.

Sequence in context: A203648 A300889 A275807 * A199267 A115290 A273842

Adjacent sequences:  A202321 A202322 A202323 * A202325 A202326 A202327

KEYWORD

nonn,cons

AUTHOR

Clark Kimberling, Dec 16 2011

STATUS

approved

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Last modified March 25 22:28 EDT 2019. Contains 321477 sequences. (Running on oeis4.)