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%I #5 Mar 30 2012 18:57:53
%S 4,2,2,2,7,4,9,5,2,8,7,9,4,9,2,7,3,2,4,4,8,4,2,4,9,6,7,6,6,1,0,8,2,0,
%T 1,2,8,1,6,3,3,7,1,2,5,9,8,2,1,1,0,6,8,4,2,5,6,3,8,6,4,9,8,5,9,8,2,7,
%U 0,2,6,1,8,7,8,2,0,1,6,6,2,4,8,1,4,0,6,0,0,0,9,9,4,5,8,4,0,4,0
%N Decimal expansion of greatest x having x^2-4x=-2*cos(x).
%C See A197737 for a guide to related sequences. The Mathematica program includes a graph.
%e least x: 0.50130475545480646339369035756819...
%e greatest x: 4.222749528794927324484249676610...
%t a = 1; b = -4; c = -2;
%t f[x_] := a*x^2 + b*x; g[x_] := c*Cos[x]
%t Plot[{f[x], g[x]}, {x, 0, 5}]
%t r1 = x /. FindRoot[f[x] == g[x], {x, .5, .51}, WorkingPrecision -> 110]
%t RealDigits[r1] (* A198100 *)
%t r2 = x /. FindRoot[f[x] == g[x], {x, 4.2, 4.3}, WorkingPrecision -> 110]
%t RealDigits[r2] (* A198101 *)
%Y Cf. A197737.
%K nonn,cons
%O 1,1
%A _Clark Kimberling_, Oct 21 2011