A202344 - OEIS

%I #17 Nov 21 2024 15:39:24

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

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

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

%N Decimal expansion of x > 0 satisfying 3*x + 1 = exp(x).

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

%H G. C. Greubel, <a href="/A202344/b202344.txt">Table of n, a(n) for n = 1..10000</a>

%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>

%e x = 1.9038136944403834847101403608281351272...

%t u = 3; v = 1;

%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, 1.9, 2.0}, WorkingPrecision -> 110]

%t RealDigits[r]  (* A202344 *)

%t RealDigits[-1/3 - ProductLog[-1, -1/(3*E^(1/3))], 10, 99] // First (* _Jean-François Alcover_, Feb 27 2013 *)

%o (PARI) solve(x=1, 2, 3*x+1-exp(x)) \\ _Michel Marcus_, Nov 09 2017

%Y Cf. A202320.

%K nonn,cons

%O 1,2

%A _Clark Kimberling_, Dec 17 2011