A197482 - OEIS

%I #5 Mar 30 2012 18:57:52

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

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

%U 4,4,1,3,0,1,5,3,3,2,5,3,8,9,7,4,9,9,4,1,8,9,9,1,0,2,9,9,9,1,0

%N Decimal expansion of least x>0 having cos(3x)=(cos 2x)^2.

%C The Mathematica program includes a graph.  See A197476 for a guide for the least x>0 satisfying cos(b*x)=(cos(c*x))^2 for selected b and c.

%e x=1.843768176031721569639938497723621273145...

%t b = 3; c = 2; f[x_] := Cos[x]

%t t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, 1.8, 1.9}, WorkingPrecision -> 200]

%t RealDigits[t] (* A197482 *)

%t Plot[{f[b*x], f[c*x]^2}, {x, 0, 2.5}]

%Y Cf. A197476.

%K nonn,cons

%O 1,2

%A _Clark Kimberling_, Oct 15 2011