A197577 - OEIS

%I #9 Apr 10 2021 13:21:16

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

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

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

%N Decimal expansion of least x > 0 having cos(Pi*x) = cos(2*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=0.6346640839769854244680925748518944036989356...

%t b = Pi; c = 2; f[x_] := Sin[x]

%t t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, .63, .64}, WorkingPrecision -> 200]

%t RealDigits[t] (* A197577 *)

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

%Y Cf. A197133.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Oct 16 2011