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Decimal expansion of the least x satisfying -x^2+3=e^x.
3

%I #5 Mar 30 2012 18:58:02

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

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

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

%N Decimal expansion of the least x satisfying -x^2+3=e^x.

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

%e least: -1.677232708532537998892701011779421...

%e greatest: 0.8344868653087587860911016801273...

%t a = -1; b = 0; c = 3;

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

%t Plot[{f[x], g[x]}, {x, -2, 1}, {AxesOrigin -> {0, 0}}]

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

%t RealDigits[r] (* A201753 *)

%t r = x /. FindRoot[f[x] == g[x], {x, .8, .9}, WorkingPrecision -> 110]

%t RealDigits[r] (* A201754 *)

%Y Cf. A201741.

%K nonn,cons

%O 1,2

%A _Clark Kimberling_, Dec 05 2011