A202353 Decimal expansion of the number x satisfying 2*x + 2 = exp(-x), negated.

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

Offset

0,1

Comments

See A202322 for a guide to related sequences. The Mathematica program includes a graph.

Links

G. C. Greubel, Table of n, a(n) for n = 0..5000

Formula

Equals W(e/2) - 1, where W(x) is the Lambert W-function. - G. C. Greubel, Jun 09 2017

Example

x = -0.3149230578454060539717505194623698115859...

Mathematica

u = 2; v = 2;
f[x_] := u*x + v; g[x_] := E^-x
Plot[{f[x], g[x]}, {x, -1, 1}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, -.4, -.3}, WorkingPrecision -> 110]
RealDigits[r] (* A202353 *)
(* other program *)
RealDigits[ ProductLog[E/2] - 1, 10, 99] // First (* Jean-François Alcover, Feb 14 2013 *)

Prog

(PARI) lambertw(exp(1)/2) - 1 \\ G. C. Greubel, Jun 09 2017

Crossrefs

Cf. A202322.

Sequence in context: A094166 A266131 A338871 * A108621 A193792 A190179

Adjacent sequences: A202350 A202351 A202352 * A202354 A202355 A202356

Keyword

nonn,cons

Author

Clark Kimberling, Dec 18 2011

Status

approved