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%I #8 Jan 22 2013 03:03:30
%S 0,8,4,5,3,5,2,3,0,6,6,9,1,6,3,4,4,0,0,2,2,7,6,5,2,4,4,7,8,1,1,1,9,7,
%T 3,5,1,3,3,4,3,7,7,5,2,5,1,2,2,3,5,4,8,7,9,0,6,9,2,3,1,8,0,2,1,9,2,6,
%U 0,4,3,6,8,0,1,1,6,0,4,0,8,8,9,2,9,1,8,5,8,2,6,6,3,9,1,9,3,3,3,6,5
%N Decimal expansion of least x>0 having sin(2x)=(sin 5x)^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=0.08453523066916344002276524478111...
%t b = 2; c = 5; f[x_] := Sin[x]
%t t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, .06, .09}, WorkingPrecision -> 100]
%t RealDigits[t] (* A197256 *)
%t Plot[{f[b*x], f[c*x]^2}, {x, 0, Pi/2}]
%Y Cf. A197133.
%K nonn,cons
%O 0,2
%A _Clark Kimberling_, Oct 12 2011