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%I #10 Aug 09 2021 14:10:27
%S 4,8,0,7,8,7,5,9,8,2,7,9,7,1,6,9,5,2,9,0,4,8,1,9,9,1,3,7,2,7,2,5,3,5,
%T 1,0,8,1,4,6,8,1,3,4,5,3,5,8,8,3,6,7,4,7,3,8,1,4,2,7,0,6,8,2,7,7,7,5,
%U 0,5,4,8,8,6,4,3,5,7,5,6,7,3,2,2,2,7,7,9,2,1,4,1,0,7,2,6,5,4,2,9,9
%N Decimal expansion of least x>0 having sin(5x)=(sin 2x)^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=0.4807875982797169529048199137272...
%t b = 5; c = 2; f[x_] := Sin[x]
%t t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, .4, .7}, WorkingPrecision -> 100]
%t RealDigits[t] (* A197284 *)
%t Plot[{f[b*x], f[c*x]^2}, {x, 0, Pi}]
%Y Cf. A197133.
%K nonn,cons
%O 0,1
%A _Clark Kimberling_, Oct 13 2011