A197483 Decimal expansion of least x>0 having cos(3x)=(cos 4x)^2.

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

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

			0.48239509881112657723091139502456544284207...
		

Links

• Index entries for transcendental numbers.

Crossrefs

Cf. A197476.

Programs

Mathematica

b = 3; c = 4; f[x_] := Cos[x]
t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, .47, .5}, WorkingPrecision -> 200]
RealDigits[t] (* A197483 *)
Plot[{f[b*x], f[c*x]^2}, {x, 0, 0.6}]