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%I #7 Aug 03 2021 13:37:04
%S 8,5,6,3,7,4,0,4,9,7,4,4,3,4,6,1,0,9,3,2,2,0,7,8,0,6,2,5,6,4,7,2,9,1,
%T 9,9,4,7,6,6,0,0,5,0,8,8,7,5,4,8,2,4,0,9,4,3,3,1,0,1,4,8,8,7,0,6,8,7,
%U 1,6,7,3,4,6,5,9,9,3,0,2,8,3,6,5,7,7,2,0,9,8,7,5,0,6,7,2,7,4,5
%N Decimal expansion of least x satisfying x^2 + 4*x*cos(x) = 2*sin(x).
%C See A199597 for a guide to related sequences. The Mathematica program includes a graph.
%e least: -0.856374049744346109322078062564729199476600...
%e greatest: 3.515613199687358023842180210704030792217...
%t a = 1; b = 4; c = 2;
%t f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c*Sin[x]
%t Plot[{f[x], g[x]}, {x, -2, 4}, {AxesOrigin -> {0, 0}}]
%t r = x /. FindRoot[f[x] == g[x], {x, -.86, -.85}, WorkingPrecision -> 110]
%t RealDigits[r] (* A199615, least of 4 roots *)
%t r = x /. FindRoot[f[x] == g[x], {x, 3.5, 3.6}, WorkingPrecision -> 110]
%t RealDigits[r] (* A199616, greatest of 4 roots *)
%Y Cf. A199597.
%K nonn,cons
%O 0,1
%A _Clark Kimberling_, Nov 08 2011
%E a(96) onwards corrected by _Georg Fischer_, Aug 03 2021
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