For large enough runs, 0, 1, 2, ..., max, 0, 1, ... etc exhibits that behaviour. Thus, a PRNG that fails your proposal is bad, but passing it doesn't meanthat the PRNG is good. A test suite like diehard (or the moderner version dieharder) runs tests for uniform distribution as well as a lot of others, but even then, a pass is only saying "any glaring nonrandomness can't be detected by this suite".

Thanks, that's true but my comment was mostly a response to the "three million zeroes and a single four" as a valid random sequence comment. I wasn't suggesting it as a generic method to test the quality of a PRNG.