A197486 - OEIS

%I #9 Feb 27 2013 05:11:38

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

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

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

%N Decimal expansion of least x>0 having cos(4x)=(cos(8x))^2.

%C The Mathematica program includes a graph.  See A197476 for a guide for the least x>0 satisfying cos(b*x)=(cos(c*x))^2 for selected b and c.

%e x=0.284435983226363889447362465013752087396201072...

%t b = 4; c = 8; f[x_] := Cos[x]

%t t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, .28, .29}, WorkingPrecision -> 100]

%t RealDigits[t] (* A197486 *)

%t Plot[{f[b*x], f[c*x]^2}, {x, 0, 0.4}]

%t RealDigits[ 1/2*ArcTan[ Sqrt[ Root[#^3 - 5#^2 + 19# - 7&, 1]]], 10, 99] // First (* _Jean-François Alcover_, Feb 27 2013 *)

%Y Cf. A197476.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Oct 15 2011