A197266 - OEIS

%I #13 Jan 30 2013 05:41:06

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

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

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

%N Decimal expansion of least x>0 having sin(3x) = (sin 8x)^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 = 0.04919274831795689680304080307291789597077...

%t b = 3; c = 8; f[x_] := Sin[x]

%t t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, .03, .1}, WorkingPrecision -> 100]

%t RealDigits[t] (* A197266 *)

%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