you can also check that (1,1), (1,2), (2,1), and (2,2) all happen with expected frequencies (i.e. roughly 25%), where the two numbers in the pair are just two numbers in a row in the sequence. You would have gotten 100% (1,2) and 0% for the rest, so that's suspicious.

same for 3-tuples, 4-tuples, ..., and n-tuples.

There's probably other, more sophisticated tests as well, but I'm not an expert.