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%I #13 Apr 10 2021 11:48:01
%S 0,8,9,3,1,1,7,7,4,8,5,4,4,8,4,7,6,2,9,4,4,5,4,2,3,6,0,1,7,1,0,9,9,4,
%T 7,7,0,8,2,6,4,5,8,9,5,0,0,5,0,8,4,9,4,2,4,4,4,3,9,3,3,8,9,1,3,0,1,1,
%U 5,7,8,4,5,7,0,9,8,7,2,0,2,8,1,0,1,7,1,0,3,2,5,5,5,9,6,8,4,7,2
%N Decimal expansion of least x > 0 having sin(Pi*x/4) = 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=0.0893117748544847629445423601710994770...
%t b = Pi/4; c = 3; f[x_] := Sin[x]
%t t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, .08, .09}, WorkingPrecision -> 200]
%t RealDigits[t](* A197392 *)
%t Plot[{f[b*x], f[c*x]^2}, {x, 0, 0.8}]
%Y Cf. A197133.
%K nonn,cons
%O 0,2
%A _Clark Kimberling_, Oct 14 2011