A197584 Decimal expansion of least x>0 having cos(Pi*x/3)=(cos(x/3))^2.

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

Offset: 1

Author

Clark Kimberling, Oct 16 2011

Keywords

• nonn
• cons

Comments

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

Examples

			4.504574941367287652051841788658834471409543359217023376915498327810090...
		

Crossrefs

Cf. A197133.

Programs

Maple

fsolve(cos(Pi*x/3)-cos(x/3)^2,x=1..5) ; # R. J. Mathar, Oct 18 2011

PARI

solve(x=4,5,cos(Pi/3*x)-cos(x/3)^2) \\ Charles R Greathouse IV, Oct 18 2011

Formula

Equals 3*A197515. - R. J. Mathar, Oct 18 2011

Extensions

Corrected by Charles R Greathouse IV, Oct 18 2011