A197587 - OEIS

%I #9 Apr 10 2021 16:36:48

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

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

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

%N Decimal expansion of least x > 0 having cos(4*Pi*x) = cos(x)^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=0.2453040545274113938392820948690956431...

%t b = 4*Pi; c = 1; f[x_] := Sin[x]

%t t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, .24, .25}, WorkingPrecision -> 200]

%t RealDigits[t]  (* A197587 *)

%t Plot[{f[b*x], f[c*x]^2}, {x, 0, 0.6}]

%Y Cf. A197133.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Oct 16 2011