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%I #13 Jul 28 2021 03:49:17
%S 1,3,6,6,5,1,1,9,2,1,7,0,5,7,2,3,9,4,9,5,6,9,7,6,0,1,7,8,8,5,9,0,5,4,
%T 6,3,2,0,0,1,1,3,9,1,7,6,8,4,9,0,6,8,5,9,4,1,9,0,6,3,5,2,4,2,8,8,8,1,
%U 0,7,0,4,0,2,7,1,2,5,0,1,5,4,4,0,3,2,2,6,1,8,6,7,9,1,7,2,3,5,5,7,9,7,8,9,8,9,5,8,8,7,1
%N Decimal expansion of least x>0 having sin(3x)=(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 0.13665119217057239495697601788590546...
%t b = 3; c = 5; f[x_] := Sin[x]
%t t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, .1, .3}, WorkingPrecision -> 100]
%t RealDigits[t] (* A197263 *)
%t Plot[{f[b*x], f[c*x]^2}, {x, 0, 1}]
%Y Cf. A197133.
%K nonn,cons
%O 0,2
%A _Clark Kimberling_, Oct 12 2011
%E a(99) corrected and more terms from _Georg Fischer_, Jul 28 2021
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