OFFSET
1,2
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.
This number is irrational. I cannot prove it to be algebraic or transcendental. - Charles R Greathouse IV, Feb 16 2025
EXAMPLE
1.6519583136225007897646782857344472038126558395...
MATHEMATICA
b = Pi; c = 1/2; f[x_] := Cos[x]
t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, 1.65, 1.66},
WorkingPrecision -> 200]
RealDigits[t] (* A197517 *)
Plot[{f[b*x], f[c*x]^2}, {x, 0, 3}]
CROSSREFS
KEYWORD
AUTHOR
Clark Kimberling, Oct 16 2011
STATUS
approved