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%I #13 Apr 10 2021 11:31:45
%S 1,2,1,3,0,3,7,5,6,3,4,4,5,3,6,4,5,1,1,9,4,9,3,2,1,3,9,7,3,2,0,4,5,8,
%T 9,2,3,3,7,9,6,8,0,3,7,0,3,7,8,7,6,7,6,1,3,4,3,4,2,2,1,5,3,3,5,1,7,1,
%U 0,7,5,9,6,2,8,0,7,7,6,9,9,7,0,8,4,4,8,4,3,9,6,7,8,6,1,5,0,2,2
%N Decimal expansion of least x > 0 having sin(Pi*x/3) = 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=0.121303756344536451194932139732045892337968...
%t b = Pi/3; c = 3; f[x_] := Sin[x]
%t t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, 0.1, 0.2}, WorkingPrecision -> 200]
%t RealDigits[t] (* A197386 *)
%t Plot[{f[b*x], f[c*x]^2}, {x, 0, 1.2}]
%Y Cf. A197133.
%K nonn,cons
%O 0,2
%A _Clark Kimberling_, Oct 14 2011