A197264 Decimal expansion of least x>0 having sin(3x) = sin(6x)^2.

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

Offset: 0

Author

Clark Kimberling, Oct 12 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

			0.090990616412274983469538935361289943682...
		

Crossrefs

Cf. A197133.

Programs

Mathematica

b = 3; c = 6; f[x_] := Sin[x]
t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, .05, .2}, WorkingPrecision -> 100]
RealDigits[t] (* A197264 *)
Plot[{f[b*x], f[c*x]^2}, {x, 0, 0.6}]

Formula

As constants, equal to 3*A197133. - Charles R Greathouse IV, Feb 13 2025

Extensions

a(99)-a(100) corrected by Sean A. Irvine, Sep 08 2021