A197413 Decimal expansion of least x > 0 having sin(Pi*x/6) = sin(x)^2.

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

Offset: 1

Author

Clark Kimberling, Oct 14 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=1.9606696545879355939544868833157...
		

Crossrefs

Cf. A197133.

Programs

Mathematica

b = Pi/6; c = 1; f[x_] := Sin[x]
t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, 1.95, 1.97},
   WorkingPrecision -> 200]
RealDigits[t] (* A197413 *)
Plot[{f[b*x], f[c*x]^2}, {x, 1.5, 2.5}]