Of course this sequence doesn't enumerate any _negative_ numbers. So, the puzzles are:

* Can you find a nonnegative rational number that's not in this sequence?

and

* Can you find a nonnegative rational number that shows up in this sequence twice?

* Can you find a nonnegative rational number that's not in this sequence?

and

* Can you find a nonnegative rational number that shows up in this sequence twice?