Hi, Narbe,

the question defines by induction a sequence of integers in

:

and, for

,

. So

:

. And so on. The question is: give an expression for

for all

.

My advice would be to compute a few terms of the sequence and look at what happens.

The "pseudo-random numbers" thing is a reference to a well-known method of getting random numbers (or kind of) on a computer, that works with similar inductive equations (but with larger numbers than 4 and 7). To learn more (not for your exercise but personal interest), look at

this.