random number generator which produces same order for each seed, highest value not higher than cycle length & no close form for index or value

full question:
Is there a (pseudo) random number generator which produces same value order for each seed, highest value not (much) higher than cycle length & no close form to get i'th value or index of a value?

more details:
-cycle length is the number of elements until it starts again
-all numbers of that cycle should not be much higher than the cycle length itself. Lets say <100 times.
-all cycle numbers can't be stored by a usual computer
-random number equations should now allow to produce the i'th value after the seed or determine the index of a given value. Only way of computation should be the iterative way. Even if you know the source code and run-time variables
-all seeds produce a cycle with same length. Each the same order of random values. E.g. [1 4 2 3 5 ...] if seed is 1 and [2 3 5 ...] is seed is 2 (seed don't need to be equal to first random value). Optional instead of one they produce a small amount of different cycles. Lets say <100.

You know any random generator/algorithm which can do this?
(don't need to be perfect random values)