A202346 - OEIS

%I #14 Nov 21 2024 15:38:23

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

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

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

%N Decimal expansion of x > 0 satisfying 2*x + 2 = exp(x).

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

%H G. C. Greubel, <a href="/A202346/b202346.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<0:  -0.76803904701346556525568352607754...

%e x>0:  1.6783469900166606534128845120945230...

%t u = 2; v = 2;

%t f[x_] := u*x + v; g[x_] := E^x

%t Plot[{f[x], g[x]}, {x, -3, 2}, {AxesOrigin -> {0, 0}}]

%t r = x /. FindRoot[f[x] == g[x], {x, -.8, -.7}, WorkingPrecision -> 110]

%t RealDigits[r]  (* A202345 *)

%t r = x /. FindRoot[f[x] == g[x], {x, 1.6, 1.7}, WorkingPrecision -> 110]

%t RealDigits[r] (* A202346 *)

%t RealDigits[-1 - LambertW[-1, -Exp[-1]/2], 10, 100][[1]] (* _G. C. Greubel_, Nov 09 2017 *)

%o (PARI) solve(x=0, 2, 2*x+2-exp(x)) \\ _Michel Marcus_, Nov 09 2017

%Y Cf. A202320.

%K nonn,cons,changed

%O 1,2

%A _Clark Kimberling_, Dec 17 2011