A197850 - OEIS

%I #5 Mar 30 2012 18:57:53

%S 2,6,6,7,0,2,8,4,6,4,1,0,5,8,0,1,7,9,2,6,3,5,5,4,2,1,2,9,4,9,8,3,9,9,

%T 7,4,5,8,1,5,6,8,7,8,0,8,6,3,0,3,0,2,9,7,8,5,5,1,5,5,7,5,5,6,9,0,1,1,

%U 4,1,9,8,8,3,6,3,1,8,2,9,4,1,9,1,0,4,6,8,2,6,2,6,1,3,4,5,2,3,9

%N Decimal expansion of greatest x having x^2-2x=-2*cos(x).

%C See A197737 for a guide to related sequences.  The Mathematica program includes a graph.

%e least x: 1.0485583594904940957585652640454931931...

%e greatest x: 2.66702846410580179263554212949839974

%t a = 1; b = -2; c = -2;

%t f[x_] := a*x^2 + b*x; g[x_] := c*Cos[x]

%t Plot[{f[x], g[x]}, {x, 0, 3}]

%t r1 = x /. FindRoot[f[x] == g[x], {x, 1, 1.1}, WorkingPrecision -> 110]

%t RealDigits[r1] (* A197849 *)

%t r2 = x /. FindRoot[f[x] == g[x], {x, 2.6, 2.7}, WorkingPrecision -> 110]

%t RealDigits[r2] (* A197850 *)

%Y Cf. A197737.

%K nonn,cons

%O 1,1

%A _Clark Kimberling_, Oct 21 2011