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%I #8 Jan 22 2013 07:24:49
%S 2,4,8,2,0,2,9,3,0,5,3,6,7,1,0,5,5,1,0,9,2,9,7,9,2,1,7,3,8,9,8,0,7,3,
%T 2,1,7,3,3,4,9,4,7,5,1,3,2,5,8,2,3,9,5,5,5,9,3,4,7,5,1,8,2,3,9,5,7,8,
%U 9,0,9,7,2,7,9,5,8,9,2,3,5,6,4,4,1,7,3,6,1,2,1,1,9,9,9,7,5,8,4,0
%N Decimal expansion of least x>0 having sin(4x)=(sin 8x)^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=0.2482029305367105510929792173898073217...
%t b = 4; c = 8; f[x_] := Sin[x]
%t t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, .1, .3}, WorkingPrecision -> 100]
%t RealDigits[t] (* A197282 *)
%t Plot[{f[b*x], f[c*x]^2}, {x, 0, 0.4}]
%Y Cf. A197133.
%K nonn,cons
%O 0,1
%A _Clark Kimberling_, Oct 12 2011