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%I #8 Jan 22 2013 05:26:29
%S 2,3,2,3,1,0,4,3,1,5,9,3,4,5,8,2,0,4,7,8,4,2,9,1,7,6,3,5,0,2,3,9,4,5,
%T 0,7,9,7,2,1,8,7,9,5,1,0,5,1,9,9,5,3,9,4,3,9,4,9,8,2,5,8,9,4,7,2,2,7,
%U 7,1,1,5,9,7,1,6,0,9,3,1,9,5,2,6,3,4,0,1,4,2,0,3,1,2,3,3,0,2,2,9
%N Decimal expansion of least x>0 having sin(3x)=(sin 4x)^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=0.2323104315934582047842917635023945079...
%t b = 3; c = 4; f[x_] := Sin[x]
%t t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, .2, .3}, WorkingPrecision -> 100]
%t RealDigits[t] (* A197262 *)
%t Plot[{f[b*x], f[c*x]^2}, {x, 0, Pi/2}]
%Y Cf. A197133.
%K nonn,cons
%O 0,1
%A _Clark Kimberling_, Oct 12 2011
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