|
%I #17 Jun 13 2021 03:15:09
%S 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,
%T 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,
%U 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
%N Decimal expansion of greatest x satisfying 3*x = exp(x).
%C See A202320 for a guide to related sequences. The Mathematica program includes a graph.
%H G. C. Greubel, <a href="/A202352/b202352.txt">Table of n, a(n) for n = 1..10000</a>
%F Equals -LambertW(-1,-1/3). - _Gleb Koloskov_, Jun 12 2021
%e least: 0.61906128673594511215232699402092223330147...
%e greatest: 1.51213455165784247389673967807203870460...
%t u = 3; v = 0;
%t f[x_] := u*x + v; g[x_] := E^x
%t Plot[{f[x], g[x]}, {x, -1, 2}, {AxesOrigin -> {0, 0}}]
%t r = x /. FindRoot[f[x] == g[x], {x, 0.6, 0.7}, WorkingPrecision -> 110]
%t RealDigits[r] (* A202351 *)
%t r = x /. FindRoot[f[x] == g[x], {x, 1.5, 1.6}, WorkingPrecision -> 110]
%t RealDigits[r] (* A202352 *)
%t RealDigits[ -ProductLog[-1, -1/3], 10, 99] // First (* _Jean-François Alcover_, Feb 27 2013 *)
%o (PARI) solve(x=1, 2, 3*x-exp(x)) \\ _Michel Marcus_, Nov 09 2017
%Y Cf. A202320.
%K nonn,cons
%O 1,2
%A _Clark Kimberling_, Dec 17 2011
|
