A202352 Decimal expansion of greatest x satisfying 3*x = exp(x).

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

Offset: 1

Author

Clark Kimberling, Dec 17 2011

Keywords

• nonn
• cons

Comments

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

Examples

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

Links

• G. C. Greubel, Table of n, a(n) for n = 1..10000
• Index entries for transcendental numbers

Crossrefs

Cf. A202320.

Programs

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, -1/3], 10, 99] // First (* Jean-François Alcover, Feb 27 2013 *)

PARI

solve(x=1, 2, 3*x-exp(x)) \\ Michel Marcus, Nov 09 2017

Formula

Equals -LambertW(-1,-1/3). - Gleb Koloskov, Jun 12 2021