A197585 Decimal expansion of least x > 0 having cos(2*Pi*x) = cos(x)^2.

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

Offset: 0

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=0.4674563763333581675096373380169467059750...
		

Crossrefs

Cf. A197133.

Programs

Mathematica

b = 2*Pi; c = 1; f[x_] := Sin[x]
t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, .46, .47}, WorkingPrecision -> 200]
RealDigits[t]  (* A197585 *)
Plot[{f[b*x], f[c*x]^2}, {x, 0, Pi}]