A197329 Decimal expansion of least x > 0 having sin(2*x) = sin(Pi*x/3)^2.

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

Offset: 1

Author

Clark Kimberling, Oct 13 2011

Keywords

• nonn
• cons

Comments

The Mathematica program includes a graph. See A197133 for a guide to least x > 0 satisfying sin(b*x) = sin(c*x)^2 for selected b and c.

Examples

			x=1.0865840657651827174317135214300513846...
		

Crossrefs

Cf. A197133.

Programs

Mathematica

b = 2; c = Pi/3; f[x_] := Sin[x]
t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, 1, 1.5}, WorkingPrecision -> 200]
RealDigits[t]  (* A197329 *)
Plot[{f[b*x], f[c*x]^2}, {x, 0, 1.5}]