A197393 Decimal expansion of least x > 0 having sin(Pi*x/4) = sin(x/2)^2.

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

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=2.53865633590794169787237029940757761479574...
		

Crossrefs

Cf. A197133.

Programs

Mathematica

b = Pi/4; c = 1/2; f[x_] := Sin[x]
t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, 2.5, 2.6}, WorkingPrecision -> 200]
RealDigits[t](* A197393 *)
Plot[{f[b*x], f[c*x]^2}, {x, 0, 2.8}]