A197254 - OEIS

%I #8 Jan 22 2013 05:26:46

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

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

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

%N Decimal expansion of least x>0 having sin(x)=(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=0.0157068495316200650581770302085260363...

%t b = 1; c = 8; f[x_] := Sin[x]

%t t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, .01, .1}, WorkingPrecision -> 100]

%t RealDigits[t] (* A197254 *)

%t Plot[{f[b*x], f[c*x]^2}, {x, 0, 0.05}]

%Y Cf. A197133.

%K nonn,cons

%O 0,3

%A _Clark Kimberling_, Oct 12 2011