A197520 Decimal expansion of least x>0 having cos(2*Pi*x)=(cos 3x)^2.

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

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.

This number is irrational. I cannot prove it to be algebraic or transcendental. - Charles R Greathouse IV, Feb 16 2025

Examples

			0.9063622365387214175196919227588469103120887...
		

Crossrefs

Cf. A197476.

Programs

Mathematica

b = 2 Pi; c = 3; f[x_] := Cos[x]
t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, .9, .91}, WorkingPrecision -> 200]
RealDigits[t]   (* A197520 *)
Plot[{f[b*x], f[c*x]^2}, {x, 0, Pi/2}]