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%I #5 Mar 30 2012 18:58:03
%S 2,9,9,2,2,3,4,8,7,2,0,5,3,9,3,6,8,6,5,0,9,3,3,1,1,4,5,2,7,8,3,8,8,2,
%T 6,2,1,8,1,1,5,9,4,5,4,7,7,4,9,0,0,6,3,6,3,9,1,2,5,6,2,3,9,9,9,3,6,1,
%U 6,8,9,8,5,4,9,6,4,7,1,9,5,1,2,1,1,4,9,4,4,6,8,2,5,6,7,1,0,5,1
%N Decimal expansion of the greatest 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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