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 A201924 Decimal expansion of the least x satisfying x^2+4x+3=e^x. 4

%I

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

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

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

%N Decimal expansion of the least x satisfying x^2+4x+3=e^x.

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

%e least: -3.024014501135293784775589627797395351659...

%e nearest to 0: -0.79522661386054079889626155638871...

%e greatest: 3.2986275628038651802559413164923413431...

%t a = 1; b = 4; c = 3;

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

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

%t r = x /. FindRoot[f[x] == g[x], {x, -3.1, -3.0}, WorkingPrecision -> 110]

%t RealDigits[r] (* A201924 *)

%t r = x /. FindRoot[f[x] == g[x], {x, -.8, -.7}, WorkingPrecision -> 110]

%t RealDigits[r] (* A201925 *)

%t r = x /. FindRoot[f[x] == g[x], {x, 3.2, 3.3}, WorkingPrecision -> 110]

%t RealDigits[r] (* A201926 *)

%Y Cf. A201741.

%K nonn,cons

%O 1,1

%A _Clark Kimberling_, Dec 06 2011

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Last modified September 23 10:15 EDT 2021. Contains 347612 sequences. (Running on oeis4.)