A197290 Decimal expansion of least x>0 having sin(6x)=(sin x)^2.

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

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..99.

Example

x=0.4868248820126508954044126405332359296...

Mathematica

b = 6; c = 1; f[x_] := Sin[x]
t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, .4, .6}, WorkingPrecision -> 100]
RealDigits[t] (* A197290 *)
Plot[{f[b*x], f[c*x]^2}, {x, 0, Pi/2}]

Crossrefs

Cf. A197133.

Sequence in context: A063808 A081455 A279160 * A200368 A322087 A142350

Adjacent sequences: A197287 A197288 A197289 * A197291 A197292 A197293

Keyword

nonn,cons

Author

Clark Kimberling, Oct 13 2011

Extensions

Offset corrected by Georg Fischer, Aug 10 2021

Status

approved