A197492 - OEIS

%I #9 Apr 10 2021 11:45:41

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

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

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

%N Decimal expansion of least x > 0 having cos(x) = cos(Pi*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=0.811493321502496430232169554116613810...

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

%t t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, .81, .82}, WorkingPrecision -> 110]

%t RealDigits[t] (* A197492 *)

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

%Y Cf. A197476.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Oct 15 2011