Unique random number algorithm

Unique random number algorithm

I would like an algorithm/function that, given a number N, generates
random numbers from 0 to N - 1 in constant time. After the Nth call, the
function may do as it pleases. Also, it is important that the algorithm
generates the numbers when requested rather than using shuffling, because
I may (and in the average case do) not need the full list of numbers. What
is the best approach to take?
(optional to read) I thought of having a hash set of numbers, and pulling
the numbers out one at a time, but this would require inserting all
elements (which I often do not need) into the hash set first... this will
not work... Argh
Thanks for any help in advance.