A197377 Decimal expansion of least x>0 having sin(x)=(sin(x/3))^2.

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

Offset

1,1

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=1..99.

Example

x=2.54418623694444302415883301699525424022009...

Mathematica

b = 1; c = 1/3; f[x_] := Sin[x]
t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, 2.3, 2.6}, WorkingPrecision -> 200]
RealDigits[t] (* A197377 *)
Plot[{f[b*x], f[c*x]^2}, {x, 0, 2.7}]
RealDigits[ 3*ArcCos[Sqrt[7]/4], 10, 99] // First (* Jean-François Alcover, Feb 19 2013 *)

Crossrefs

Cf. A197133.

Sequence in context: A266416 A266401 A083798 * A211247 A021397 A325941

Adjacent sequences: A197374 A197375 A197376 * A197378 A197379 A197380

Keyword

nonn,cons

Author

Clark Kimberling, Oct 14 2011

Status

approved