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A201897 Decimal expansion of the least x satisfying x^2+3x+1=e^x. 4

%I

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

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

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

%N Decimal expansion of the least x satisfying x^2+3x+1=e^x.

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

%e least: -2.1093569955710161272316992470592578841155...

%e nearest to 0: -0.608989103010165494835043701926011...

%e greatest: 2.99223487205393686509331145278388262181...

%t a = 1; b = 3; c = 2;

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

%t Plot[{f[x], g[x]}, {x, -3, 3.1}, {AxesOrigin -> {0, 0}}]

%t r = x /. FindRoot[f[x] == g[x], {x, -2.2, -2.1}, WorkingPrecision -> 110]

%t RealDigits[r] (* A201897, least *)

%t r = x /. FindRoot[f[x] == g[x], {x, -.7, -.6}, WorkingPrecision -> 110]

%t RealDigits[r] (* A201898, nearest 0 *)

%t r = x /. FindRoot[f[x] == g[x], {x, 2.9, 3.0}, WorkingPrecision -> 110]

%t RealDigits[r] (* A201899 greatest *)

%Y Cf. A201741.

%K nonn,cons

%O 1,1

%A _Clark Kimberling_, Dec 06 2011

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Last modified January 25 04:15 EST 2022. Contains 350565 sequences. (Running on oeis4.)