[seqfan] fractal sequences

[Kimberling, Clark]

I'm hoping someone can shed some light on fractal sequences - here's the
question:  

If V(x) is the lower trim of a fractal sequence x, and if V(x)=x, 
what can be said about x?

It is known that V(x)=x when x is a signature sequence of a positive
irrational number.  

Recall that the UPPER trim of x is x itself, but the LOWER trim of x,
although 
fractal sequence, need not be identical to x.

Example:  A0084531 is the signature sequence of the golden ratio:
1, 2, 1, 3, 2, 4, 1, 3, 5, 2, 4, 1, 6, 3, 5, 2, 7,...
The upper trim is what's left after deleting the first occurrence of
each n.
The lower trim is what's left after subtracting 1 from all terms and
then deleting all 0s.

Clark Kimberling