About a new family of sequences
  First we define a new kind of function over $\mathbb{N}$. For each $i\in\mathbb{N}$ we have an associated function, which will be called $S_i$ . Then we define a new kind of sequence, to be made from the functions $S_i$ . Finally, we will see that some of these sequences has a self-similarity feature. 
Felipe Bottega Diniz
math.GM