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 A201933 Decimal expansion of the least x satisfying x^2+5x+2=e^x. 4

%I

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

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

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

%N Decimal expansion of the least x satisfying x^2+5x+2=e^x.

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

%e least: -4.5640783603793772013414868523420...

%e nearest to 0: -0.259069533051109108686405...

%e greatest: 3.43200871161068035280379146269...

%t a = 1; b = 5; c = 2;

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

%t Plot[{f[x], g[x]}, {x, -5, 3.5}, {AxesOrigin -> {0, 0}}]

%t r = x /. FindRoot[f[x] == g[x], {x, -4.6, -4.5}, WorkingPrecision -> 110]

%t RealDigits[r] (* A201933 *)

%t r = x /. FindRoot[f[x] == g[x], {x, -.3, -.2}, WorkingPrecision -> 110]

%t RealDigits[r] (* A201934 *)

%t r = x /. FindRoot[f[x] == g[x], {x, 3.4, 3.5}, WorkingPrecision -> 110]

%t RealDigits[r] (* A201935 *)

%Y Cf. A201741.

%K nonn,cons

%O 1,1

%A _Clark Kimberling_, Dec 06 2011

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