A197478 Decimal expansion of least x>0 having cos(x)=(cos 4x)^2.

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

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

			0.6653753198206945999410976241416973212944400...
		

Links

• Index entries for transcendental numbers.

Crossrefs

Cf. A197476.

Programs

Mathematica

b = 1; c = 4; f[x_] := Cos[x]
t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, .6, .7}, WorkingPrecision -> 200]
RealDigits[t] (* A197478 *)
Plot[{f[b*x], f[c*x]^2}, {x, 0, 1}]