[haypo]
> What is an uninteresting sequence? What are the problem of these
> sequences?

A sequence that would greatly surprise a user.  For example, if you generate 32-bit ints from the Twister in one obvious way, there are starting places where you'll get 623 zeroes in a row.  And places where you'll get 2**32-1 623 times in a row.  Pick a sequence of any 623 32-bit ints, and there's a starting place that will deliver that sequence.  And, indeed, a truly random sequence must also display that behavior, but it's nevertheless very surprising when you see one.  It's very rare, both in a truly random sequence and in sequences derived from the Twister.