[seqfan] Fractal sequence?

[David Sycamore]

Dear Seqfans,

I would appreciate some clarification about the following draft sequence:

a(0)=0. If a(n)=k is the first occurrence of k then a(n+1)=a(k), else a(n+1)=n-m where m is the index of the greatest prior term.

0,0,1,0,1,2,1,1,2,3,0,1,2,3,4,1,1,2,3,4,5,2,1,2,3...

This seems to have the property of self containment, since subsequence a(T(k+1));  k>=0 looks like a copy of the original, but when the first occurrence of every k is erased, the result is not the original.

However, if a(0) and the copy subsequence are erased the result is A002260, a fractal sequence. 

So strictly speaking is this sequence fractal or not, and either way, should it go in oeis ?

Best,

David.