A197264 - OEIS

%I #12 Sep 08 2021 21:23:20

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

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

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

%N Decimal expansion of least x>0 having sin(3x) = sin(6x)^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=0.090990616412274983469538935361289943682...

%t b = 3; c = 6; f[x_] := Sin[x]

%t t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, .05, .2}, WorkingPrecision -> 100]

%t RealDigits[t] (* A197264 *)

%t Plot[{f[b*x], f[c*x]^2}, {x, 0, 0.6}]

%Y Cf. A197133.

%K nonn,cons

%O 0,2

%A _Clark Kimberling_, Oct 12 2011

%E a(99)-a(100) corrected by _Sean A. Irvine_, Sep 08 2021