A197478 - OEIS

%I #5 Mar 30 2012 18:57:52

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

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

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

%N Decimal expansion of least x>0 having cos(x)=(cos 4x)^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=0.6653753198206945999410976241416973212944400...

%t b = 1; c = 4; f[x_] := Cos[x]

%t t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, .6, .7}, WorkingPrecision -> 200]

%t RealDigits[t] (* A197478 *)

%t Plot[{f[b*x], f[c*x]^2}, {x, 0, 1}]

%Y Cf. A197476.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Oct 15 2011