A197581 Decimal expansion of least x > 0 having cos(Pi*x/2) = cos(x/2)^2.

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

Offset: 1

Author

Clark Kimberling, Oct 16 2011

Keywords

• nonn
• cons

Comments

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.

Examples

			x=1.640686147655524949712399177419809610113...
		

Crossrefs

Cf. A197133.

Programs

Mathematica

b = Pi/2; c = 1/2; f[x_] := Sin[x]
t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, 1.64, 1.641},
   WorkingPrecision -> 200]
RealDigits[t] (* A197581 *)
Plot[{f[b*x], f[c*x]^2}, {x, 0, 2}]