A197380 Decimal expansion of least x > 0 having sin(Pi*x/3) = sin(Pi*x/6)^2.

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

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=2.1144982940974003549475935426515568442931... [corrected by _Georg Fischer_, Jul 28 2021]
		

Crossrefs

Cf. A197133.

Programs

Mathematica

b = Pi/3; c = Pi/6; f[x_] := Sin[x]
t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, 2.3, 2.6}, WorkingPrecision -> 200]
RealDigits[t] (* A197380 *)
Plot[{f[b*x], f[c*x]^2}, {x, 0, 2.7}]
RealDigits[ 6*ArcCos[1/Sqrt[5]]/Pi, 10, 99] // First (* Jean-François Alcover, Feb 19 2013 *)