A197332 Decimal expansion of least x > 0 having sin(3*x) = sin(Pi*x/3)^2.

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

Offset: 0

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=0.8367163121639918677342139299267028496795515...
		

Crossrefs

Cf. A197133.

Programs

Mathematica

b = 3; c = Pi/3; f[x_] := Sin[x]
t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, .8, 1}, WorkingPrecision -> 200]
RealDigits[t]   (* A197332 *)
Plot[{f[b*x], f[c*x]^2}, {x, 0, 1.5}]