A197577 Decimal expansion of least x > 0 having cos(Pi*x) = cos(2*x)^2.

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

Offset: 0

Author

Clark Kimberling, Oct 16 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

			x=0.6346640839769854244680925748518944036989356...
		

Crossrefs

Cf. A197133.

Programs

Mathematica

b = Pi; c = 2; f[x_] := Sin[x]
t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, .63, .64}, WorkingPrecision -> 200]
RealDigits[t] (* A197577 *)
Plot[{f[b*x], f[c*x]^2}, {x, 0, 1}]