A197586 Decimal expansion of least x>0 having cos(3*Pi*x) = (cos x)^2.

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

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=0.3226477637734245926813896345699080965614970733550...
		

Crossrefs

Cf. A197133.

Programs

Mathematica

b = 3*Pi; c = 1; f[x_] := Sin[x]
t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, .32, .33}, WorkingPrecision -> 200]
RealDigits[t]  (* A197586 *)
Plot[{f[b*x], f[c*x]^2}, {x, 0, Pi}]