A197293 - OEIS

%I #10 Aug 09 2021 14:12:28

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

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

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

%N Decimal expansion of least x>0 having sin(6x)=(sin 4x)^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=0.32512030910880909604777758636733525744...

%t b = 6; c = 4; f[x_] := Sin[x]

%t t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, .3, .4}, WorkingPrecision -> 100]

%t RealDigits[t] (* A197293 *)

%t Plot[{f[b*x], f[c*x]^2}, {x, 0, Pi/4}]

%Y Cf. A197133.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Oct 13 2011