A202346 Decimal expansion of x > 0 satisfying 2*x + 2 = exp(x).

1, 6, 7, 8, 3, 4, 6, 9, 9, 0, 0, 1, 6, 6, 6, 0, 6, 5, 3, 4, 1, 2, 8, 8, 4, 5, 1, 2, 0, 9, 4, 5, 2, 3, 0, 8, 4, 8, 2, 4, 4, 5, 8, 7, 6, 5, 3, 5, 1, 6, 0, 2, 2, 1, 6, 3, 9, 8, 3, 4, 1, 8, 6, 8, 3, 9, 9, 0, 4, 7, 6, 4, 5, 6, 8, 5, 7, 1, 3, 4, 3, 6, 9, 9, 7, 4, 6, 9, 8, 2, 4, 1, 8, 8, 1, 2, 0, 6, 3

Offset

1,2

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

Example

x<0:  -0.76803904701346556525568352607754...
x>0:  1.6783469900166606534128845120945230...

Mathematica

u = 2; v = 2;
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, -.8, -.7}, WorkingPrecision -> 110]
RealDigits[r]  (* A202345 *)
r = x /. FindRoot[f[x] == g[x], {x, 1.6, 1.7}, WorkingPrecision -> 110]
RealDigits[r] (* A202346 *)
RealDigits[-1 - LambertW[-1, -Exp[-1]/2], 10, 100][[1]] (* G. C. Greubel, Nov 09 2017 *)

Prog

(PARI) solve(x=0, 2, 2*x+2-exp(x)) \\ Michel Marcus, Nov 09 2017

Crossrefs

Cf. A202320.

Sequence in context: A010500 A175639 A256922 * A117022 A051994 A085661

Adjacent sequences: A202343 A202344 A202345 * A202347 A202348 A202349

Keyword

nonn,cons

Author

Clark Kimberling, Dec 17 2011

Status

approved