A197330 Decimal expansion of least x > 0 having sin(2*x) = sin(Pi*x/4)^2.

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

Offset: 1

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=1.20938610287170523425443044462680491606...
		

Crossrefs

Cf. A197133.

Programs

Mathematica

b = 2; c = Pi/4; f[x_] := Sin[x]
t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, 1, 1.5}, WorkingPrecision -> 200]
RealDigits[t]  (* A197330 *)
Plot[{f[b*x], f[c*x]^2}, {x, 0, 1.5}]