%I #12 Apr 10 2021 11:46:50
%S 3,9,4,2,6,8,2,5,8,5,3,5,5,9,1,5,9,0,5,6,3,3,0,9,1,5,4,5,7,5,1,3,7,7,
%T 4,0,9,5,5,0,1,7,2,9,4,0,8,4,1,8,3,4,3,9,7,9,6,1,7,3,6,5,7,1,0,4,6,0,
%U 0,7,0,3,2,6,3,8,1,8,2,0,2,5,0,1,0,2,9,6,6,1,0,1,0,2,0,3,1,9,9
%N Decimal expansion of least x > 0 having cos(2*x) = cos(3*Pi*x)^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=0.3942682585355915905633091545751377409550...
%t b = 2; c = 3 Pi; f[x_] := Cos[x]
%t t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, .3, .4}, WorkingPrecision -> 110]
%t RealDigits[t] (* A197507 *)
%t Plot[{f[b*x], f[c*x]^2}, {x, 0, Pi/6}]
%Y Cf. A197476.
%K nonn,cons
%O 0,1
%A _Clark Kimberling_, Oct 15 2011