A202351 Decimal expansion of least x satisfying 3*x = exp(x).

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

Offset

0,1

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 = 0..9999 [Offset shifted by Georg Fischer, Oct 18 2021]

Example

least:  0.61906128673594511215232699402092223330147...
greatest:  1.51213455165784247389673967807203870460...

Mathematica

u = 3; v = 0;
f[x_] := u*x + v; g[x_] := E^x
Plot[{f[x], g[x]}, {x, -1, 2}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, 0.6, 0.7}, WorkingPrecision -> 110]
RealDigits[r] (* A202351 *)
r = x /. FindRoot[f[x] == g[x], {x, 1.5, 1.6}, WorkingPrecision -> 110]
RealDigits[r] (* A202352 *)
RealDigits[ -ProductLog[-1/3], 10, 99] // First (* Jean-François Alcover, Feb 27 2013 *)

Prog

(PARI) solve(x=0, 1, 3*x-exp(x)) \\ Michel Marcus, Nov 09 2017

Crossrefs

Cf. A202320.

Sequence in context: A140248 A336696 A127169 * A111507 A117236 A349141

Adjacent sequences: A202348 A202349 A202350 * A202352 A202353 A202354

Keyword

nonn,cons

Author

Clark Kimberling, Dec 17 2011

Extensions

Offset corrected by Georg Fischer, Aug 02 2021

Status

approved