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

%I #7 Mar 30 2012 18:58:02

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

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

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

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

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

%e x=2.2041177331716202959909548777323849535865...

%t a = 1; b = 1; c = 2;

%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, 2.2, 2.3}, WorkingPrecision -> 110]

%t RealDigits[r] (* A201396 *)

%Y Cf. A201741.

%K nonn,cons

%O 1,1

%A _Clark Kimberling_, Dec 06 2011