A197479 Decimal expansion of least x>0 having cos(2x)=(cos 3x)^2.

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

Offset: 0

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.

Examples

			0.681089818242874006185052816327828524925...
		

Links

• Index entries for transcendental numbers.

Crossrefs

Cf. A197476.

Programs

Mathematica

b = 2; c = 3; f[x_] := Cos[x]
t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, .6, .8}, WorkingPrecision -> 200]
RealDigits[t] (* A197479 *)
Plot[{f[b*x], f[c*x]^2}, {x, 0, 1}]