A197378 Decimal expansion of least x>0 having sin(x)=(sin(2x/3))^2.

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

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

			1.9507218546528545762866655182040115446450...
		

Links

• Index entries for transcendental numbers.

Crossrefs

Cf. A197133.

Programs

Mathematica

b = 1; c = 2/3; f[x_] := Sin[x]
t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, 2.3, 2.6}, WorkingPrecision -> 200]
RealDigits[t] (* A197378 *)
Plot[{f[b*x], f[c*x]^2}, {x, 0, 2.7}]
RealDigits[ 3*ArcCos[Root[1 - 8 #^2 + 16 #^6 &, 4]], 10, 99] // First (* Jean-François Alcover, Feb 19 2013 *)