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Decimal expansion of least x > 0 having sin(Pi*x/3) = sin(x)^2.
2

%I #13 Apr 10 2021 11:30:53

%S 1,5,4,0,6,7,5,0,0,2,9,3,4,0,1,2,5,1,0,8,8,0,4,7,8,2,3,9,5,2,2,4,3,4,

%T 3,4,4,3,8,8,3,9,4,1,0,2,0,4,5,4,5,6,5,9,8,2,5,0,3,9,3,5,7,5,6,3,9,3,

%U 4,3,1,2,7,5,8,0,4,6,1,6,2,9,3,8,1,4,7,6,2,0,9,3,9,5,9,1,4,9,0

%N Decimal expansion of least x > 0 having sin(Pi*x/3) = sin(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=1.54067500293401251088047823952243434438839410204...

%t b = Pi/3; c = 1; f[x_] := Sin[x]

%t t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, 1.5, 1.6}, WorkingPrecision -> 200]

%t RealDigits[t] (* A197384 *)

%t Plot[{f[b*x], f[c*x]^2}, {x, 1.2, 1.9}]

%Y Cf. A197133.

%K nonn,cons

%O 1,2

%A _Clark Kimberling_, Oct 14 2011