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%I #10 Aug 09 2021 14:09:20
%S 3,0,3,8,9,0,4,1,6,4,3,4,4,2,6,1,1,6,8,6,8,0,6,5,3,3,9,5,8,6,5,2,0,4,
%T 0,2,9,4,0,7,7,8,4,6,0,7,2,6,8,8,6,8,2,0,5,2,6,4,5,7,8,4,0,0,4,7,6,0,
%U 3,5,2,6,4,5,0,0,7,5,7,2,5,9,6,5,9,4,1,5,5,4,7,6,1,0,6,9,6,2,2,6,9
%N Decimal expansion of least x>0 having sin(4x)=(sin 6x)^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=0.3038904164344261168680653395865204029407784...
%t b = 4; c = 6; f[x_] := Sin[x]
%t t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, .3, .5}, WorkingPrecision -> 100]
%t RealDigits[t] (* A197270 *)
%t Plot[{f[b*x], f[c*x]^2}, {x, 0, Pi/4}]
%Y Cf. A197133.
%K nonn,cons
%O 0,1
%A _Clark Kimberling_, Oct 12 2011
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