  We investigate the conditions on an integer sequence f(n), n 2 N, with f(1) =
0, such that the sequence q(n), computed recursively via q(n) = q(n - q(n - 1))
+ f(n), with q(1) = 1, exists. We prove that f(n + 1) - f(n) in {0,1}, n > 0,
is a sufficient but not necessary condition for the existence of sequence q.
Sequences q defined in this way typically display non-trivial dynamics: in
particular, they are generally aperiodic with no obvious patterns. We discuss
and illustrate this behaviour with some examples.
