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

%I #16 Apr 10 2021 11:33:35

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

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

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

%N Decimal expansion of least x > 0 having sin(3*x) = sin(Pi*x/3)^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=0.8367163121639918677342139299267028496795515...

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

%t t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, .8, 1}, WorkingPrecision -> 200]

%t RealDigits[t] (* A197332 *)

%t Plot[{f[b*x], f[c*x]^2}, {x, 0, 1.5}]

%Y Cf. A197133.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Oct 13 2011