OFFSET
0,1
COMMENTS
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.
EXAMPLE
x=0.284435983226363889447362465013752087396201072...
MATHEMATICA
b = 4; c = 8; f[x_] := Cos[x]
t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, .28, .29}, WorkingPrecision -> 100]
RealDigits[t] (* A197486 *)
Plot[{f[b*x], f[c*x]^2}, {x, 0, 0.4}]
RealDigits[ 1/2*ArcTan[ Sqrt[ Root[#^3 - 5#^2 + 19# - 7&, 1]]], 10, 99] // First (* Jean-François Alcover, Feb 27 2013 *)
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Oct 15 2011
STATUS
approved