A197493 - OEIS

%I #9 Apr 10 2021 11:45:58

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

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

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

%N Decimal expansion of least x > 0 having cos(x) = cos(Pi*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=1.32698009211327464157967233383038042664300...

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

%t t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, 1.32, 1.33},

%t    WorkingPrecision -> 110]

%t RealDigits[t] (* A197493 *)

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

%Y Cf. A197476.

%K nonn,cons

%O 1,2

%A _Clark Kimberling_, Oct 15 2011