A197517 - OEIS

%I #5 Mar 30 2012 18:57:53

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

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

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

%N Decimal expansion of least x>0 having cos(Pi*x)=(cos x/2)^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=1.6519583136225007897646782857344472038126558395...

%t b = Pi; c = 1/2; f[x_] := Cos[x]

%t t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, 1.65, 1.66},

%t    WorkingPrecision -> 200]

%t RealDigits[t]  (* A197517 *)

%t Plot[{f[b*x], f[c*x]^2}, {x, 0, 3}]

%Y Cf. A197476.

%K nonn,cons

%O 1,2

%A _Clark Kimberling_, Oct 16 2011