%I #15 Apr 10 2021 11:34:29

%S 9,6,7,9,1,9,9,1,7,1,6,2,8,4,0,1,2,4,6,1,0,7,0,3,7,5,3,8,3,1,8,3,0,1,

%T 7,4,1,3,5,2,2,3,3,0,3,9,8,2,9,3,4,7,6,7,0,1,7,9,1,5,6,8,1,4,0,9,1,6,

%U 1,9,1,7,8,8,2,1,0,4,5,9,5,3,9,4,9,3,7,5,7,7,2,1,1,6,6,9,3,1,0

%N Decimal expansion of least x > 0 having sin(3*x) = sin(Pi*x/6)^2.

%C The Mathematica program includes a graph. See A197133 for a guide to least x > 0 satisfying sin(b*x) = sin(c*x)^2 for selected b and c.

%e x=0.967919917162840124610703753831830174...

%t b = 3; c = Pi/6; f[x_] := Sin[x]

%t t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, .8, 1}, WorkingPrecision -> 200]

%t RealDigits[t] (* *)

%t Plot[{f[b*x], f[c*x]^2}, {x, 0, 1.2}]

%Y Cf. A197133.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Oct 14 2011