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%I #12 Apr 10 2021 13:20:16
%S 1,4,9,5,9,0,9,5,4,6,4,3,9,9,9,4,8,5,7,4,9,6,5,7,5,1,8,6,3,1,6,9,6,8,
%T 0,9,1,1,9,8,1,3,6,9,1,3,1,7,2,9,0,6,0,5,8,0,7,1,1,0,0,7,9,7,7,0,8,4,
%U 0,5,9,6,7,6,1,5,8,4,6,4,0,5,7,9,6,1,3,1,5,9,5,9,2,5,2,3,7,8,5
%N Decimal expansion of least x > 0 having sin(Pi*x/6) = sin(2*x/3)^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=1.4959095464399948574965751863169680911...
%t b = Pi/6; c = 2/3; f[x_] := Sin[x]
%t t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, 1.49, 1.5}, WorkingPrecision -> 200]
%t RealDigits[t] (* A197418 *)
%t Plot[{f[b*x], f[c*x]^2}, {x, 0, 3}]
%Y Cf. A197133.
%K nonn,cons
%O 1,2
%A _Clark Kimberling_, Oct 14 2011
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