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Decimal expansion of least x > 0 having sin(Pi*x/4) = sin(3*x)^2.
2

%I #13 Apr 10 2021 11:48:01

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

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

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

%N Decimal expansion of least x > 0 having sin(Pi*x/4) = sin(3*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=0.0893117748544847629445423601710994770...

%t b = Pi/4; c = 3; f[x_] := Sin[x]

%t t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, .08, .09}, WorkingPrecision -> 200]

%t RealDigits[t](* A197392 *)

%t Plot[{f[b*x], f[c*x]^2}, {x, 0, 0.8}]

%Y Cf. A197133.

%K nonn,cons

%O 0,2

%A _Clark Kimberling_, Oct 14 2011