%I
%S 3,5,2,1,3,3,7,8,2,9,5,7,1,7,1,5,6,9,8,6,9,1,9,8,8,5,6,4,4,5,4,9,1,7,
%T 9,7,7,3,0,9,1,8,1,3,9,4,7,3,3,6,8,8,7,1,9,5,4,9,1,8,4,8,6,2,5,1,5,5,
%U 9,0,6,0,9,6,1,0,2,5,9,8,8,8,9,7,4,9,7,5,6,9,0,0,3,9,4,9,7,1,5
%N Decimal expansion of least x>0 having cos(Pi*x/2)=(cos Pi*x/3)^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.
%C Conjecture: the constant here, 3.52133782..., is 3 plus the constant in A197383, the latter being the least t>0 satisfying sin(pi*t/6)=(sin pi*t/3)^2.
%e x=3.521337829571715698691988564454917977309181394...
%t b = Pi/2; c = Pi/3; f[x_] := Cos[x]
%t t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, 3.5, 3.53}, WorkingPrecision > 200]
%t RealDigits[t] (* A197521, appears to be 3+A197383 *)
%t Plot[{f[b*x], f[c*x]^2}, {x, 0, 4}]
%t RealDigits[ 6*ArcCos[ Root[ 1  4# + 4#^3 & , 2]]/Pi, 10, 99] // First (* _JeanFrançois Alcover_, Feb 19 2013 *)
%Y Cf. A197476.
%K nonn,cons
%O 1,1
%A _Clark Kimberling_, Oct 16 2011
