A197386 - OEIS

%I #13 Apr 10 2021 11:31:45

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

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

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

%N Decimal expansion of least x > 0 having sin(Pi*x/3) = 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=0.121303756344536451194932139732045892337968...

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

%t t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, 0.1, 0.2}, WorkingPrecision -> 200]

%t RealDigits[t] (* A197386 *)

%t Plot[{f[b*x], f[c*x]^2}, {x, 0, 1.2}]

%Y Cf. A197133.

%K nonn,cons

%O 0,2

%A _Clark Kimberling_, Oct 14 2011