A197583 Decimal expansion of least x > 0 having cos(Pi*x/3) = (cos(2*x))^2.

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

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

			1.120915682254854303221593758136799146010322927947952326585665475083271...
		

Crossrefs

Cf. A197133.

Programs

Maple

Digits := 100 ; fsolve( cos(Pi*x/3)-(cos(2*x))^2,x=0.1..1.4) ; # R. J. Mathar, Oct 18 2011

Mathematica

RealDigits[x/.FindRoot[Cos[Pi x/3]==(Cos[2x])^2,{x,1},WorkingPrecision-> 100]][[1]] (* Harvey P. Dale, Apr 08 2015 *)

PARI

solve(x=1,2,cos(Pi/3*x)-cos(x+x)^2) \\ Charles R Greathouse IV, Oct 18 2011

Extensions

Corrected by Charles R Greathouse IV, Oct 18 2011