gsuberland, something that's been bouncing around in my head for a few days: I wonder if any of the common permuted congruential generators (PCGs) have the property that for any finite sequence of unique integers there is always a set of parameters (seed, multiplier, increment, modulus, shift amount, rotation amount) that produces that sequence.
I know it's not the case for LCGs, but the permutation step changes the details quite a bit.