A197494 Decimal expansion of least x>0 having cos(x)=(cos(Pi*x/3))^2.

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

Offset: 1

Author

Clark Kimberling, Oct 15 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

			1.566023613622289702303820823948946110500...
		

Crossrefs

Cf. A197476.

Programs

Mathematica

b = 1; c = Pi/3; f[x_] := Cos[x]
t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, 1.5, 1.6}, WorkingPrecision -> 110]
RealDigits[t] (* A197494 *)
Plot[{f[b*x], f[c*x]^2}, {x, 0, 2}]