%I #5 Mar 30 2012 18:58:03
%S 6,0,8,9,8,9,1,0,3,0,1,0,1,6,5,4,9,4,8,3,5,0,4,3,7,0,1,9,2,6,0,1,1,8,
%T 7,3,3,9,7,1,1,5,3,1,7,1,1,4,2,7,7,5,0,7,0,9,4,1,6,7,7,0,2,8,8,2,2,0,
%U 7,5,9,0,4,7,1,1,3,8,2,0,5,4,3,8,1,1,3,1,0,3,9,7,3,5,4,5,1,4,0
%N Decimal expansion of the x nearest 0 that satisfies 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 0,1
%A _Clark Kimberling_, Dec 06 2011
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