What do you call such an infinite sequence? $ (x_n) _ {n in Bbb N}: forall a = (x_i, x_ {i + 1}, x_ {i + 2}, …, x_ {i + j}) exists b = (x_k, x_ {k + 1}, x_ {k + 2}, …, x_ {k + j}); i not = k: a = b $

For example, the 2-adic rating of 2n, https://oeis.org/A001511

In other words, every part of the sequence has a copy of itself in the sequence. In fact, each part would have an infinite number of copies of itself. I thought that was a fractal sequence, but that's not the case.