A197293 Decimal expansion of least x>0 having sin(6x)=(sin 4x)^2.

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

Offset

0,1

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.

Links

Table of n, a(n) for n=0..100.

Example

x=0.32512030910880909604777758636733525744...

Mathematica

b = 6; c = 4; f[x_] := Sin[x]
t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, .3, .4}, WorkingPrecision -> 100]
RealDigits[t] (* A197293 *)
Plot[{f[b*x], f[c*x]^2}, {x, 0, Pi/4}]

Crossrefs

Cf. A197133.

Sequence in context: A248849 A172216 A121490 * A099643 A224344 A113260

Adjacent sequences: A197290 A197291 A197292 * A197294 A197295 A197296

Keyword

nonn,cons

Author

Clark Kimberling, Oct 13 2011

Status

approved