Fractal sequence

In mathematics, a fractal sequence is, loosely speaking, one that contains iself as a proper subsequence. An example is the sequence

   1, 2, 1, 2, 3, 1, 2, 3, 4, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 6, ...

If the first occurrence of each n is deleted, the remaining sequence is identical to the original. The process can be repeated indefinitely, so that the original sequence contains itself propertly infinitely many times.