A201889 - OEIS

%I #10 Feb 07 2025 16:44:07

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

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

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

%N Decimal expansion of the number x satisfying x^2+x+5=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 2.71287718703731960221880534853920451356941...

%t a = 1; b = 1; c = 5;

%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, 2.7, 2.8}, WorkingPrecision -> 110]

%t RealDigits[r]     (* A201889 *)

%Y Cf. A201741.

%K nonn,cons,changed

%O 1,1

%A _Clark Kimberling_, Dec 06 2011