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.