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%I #12 Apr 10 2021 13:19:30
%S 0,5,8,7,7,5,0,5,6,2,2,4,6,2,9,9,5,0,9,7,7,6,4,4,1,4,2,2,4,2,5,9,4,8,
%T 4,2,4,0,9,2,7,7,4,9,0,1,9,2,7,3,1,7,9,3,6,4,3,0,6,4,7,4,3,2,6,6,6,5,
%U 3,6,9,2,4,4,8,5,1,6,4,0,7,6,4,5,9,9,9,1,5,3,3,0,2,2,3,7,5,0,0
%N Decimal expansion of least x > 0 having sin(Pi*x/6) = sin(3*x)^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=0.0587750562246299509776441422425948...
%t b = Pi/6; c = 3; f[x_] := Sin[x]
%t t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, 0.05, 0.06},
%t WorkingPrecision -> 200]
%t RealDigits[t] (* A197415 *)
%t Plot[{f[b*x], f[c*x]^2}, {x, 0, 0.2}]
%Y Cf. A197133.
%K nonn,cons
%O 0,2
%A _Clark Kimberling_, Oct 14 2011
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