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=0.34054490912143700309252640816391426246259292812...
MATHEMATICA
b = 4; c = 6; f[x_] := Cos[x]
t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, .34, .35}, WorkingPrecision -> 100]
RealDigits[t] (* A197485 *)
Plot[{f[b*x], f[c*x]^2}, {x, 0, 1/2}]
RealDigits[ ArcTan[ Sqrt[ Root[7#^4 - 68#^3 + 106#^2 - 68# + 7&, 1] ] ], 10, 99] // First (* Jean-François Alcover, Feb 27 2013 *)
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Oct 15 2011
STATUS
approved