A197849 - OEIS

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

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

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

%U 8,8,9,5,6,0,0,5,9,0,8,9,1,7,5,2,4,4,2,1,8,2,9,9,7,0,9,5,4,0,1

%N Decimal expansion of least 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: 1.048558359490494095758565264045...

%e greatest x: 2.667028464105801792635542129...

%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 1,3

%A _Clark Kimberling_, Oct 21 2011