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%I #5 Mar 30 2012 18:57:58
%S 3,7,4,6,1,6,8,5,6,5,5,2,8,2,2,1,3,4,0,6,8,7,0,1,3,5,6,0,5,2,7,5,9,6,
%T 9,7,8,8,5,6,5,4,6,3,8,9,1,5,6,5,1,1,2,9,8,1,8,6,5,6,4,7,4,8,5,8,6,8,
%U 4,6,3,2,8,1,8,3,2,6,3,6,7,2,5,2,8,2,4,8,1,0,6,7,7,2,4,4,1,6,4
%N Decimal expansion of least x satisfying x^2-4*x*cos(x)=3*sin(x).
%C See A199597 for a guide to related sequences. The Mathematica program includes a graph.
%e least: -3.746168565528221340687013560527596978856...
%e greatest: 1.625278383378448643933003226246836106...
%t a = 1; b = -4; c = 3;
%t f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c*Sin[x]
%t Plot[{f[x], g[x]}, {x, -4, 2}, {AxesOrigin -> {0, 0}}]
%t r = x /. FindRoot[f[x] == g[x], {x, -3.8, -3.7}, WorkingPrecision -> 110]
%t RealDigits[r] (* A199733 least root *)
%t r = x /. FindRoot[f[x] == g[x], {x, 1.6, 1.7}, WorkingPrecision -> 110]
%t RealDigits[r] (* A199734 greatest root *)
%Y Cf. A199597.
%K nonn,cons
%O 1,1
%A _Clark Kimberling_, Nov 09 2011
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