A201772 - OEIS

%I #8 Jan 30 2025 11:24:41

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

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

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

%N Decimal expansion of the number x satisfying x^2+x+4=e^x.

%C See A201741 for a guide to related sequences.  The Mathematica program includes a graph.

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

%e 2.58555463371173779562468636302780677323083330000...

%t a = 1; b = 1; c = 4;

%t f[x_] := a*x^2 + b*x + c; g[x_] := E^x

%t Plot[{f[x], g[x]}, {x, -1, 3}, {AxesOrigin -> {0, 0}}]

%t r = x /. FindRoot[f[x] == g[x], {x, 2.5, 2.6}, WorkingPrecision -> 110]

%t RealDigits[r]     (* A201772 *)

%Y Cf. A201741.

%K nonn,cons,changed

%O 1,1

%A _Clark Kimberling_, Dec 06 2011