Those tests can "disprove" that a sequence is random (quotes because of course a true random generator will occasionally generate suspicious sequences of arbit

Those tests can "disprove" that a sequence is random (quotes because of course a true random generator will occasionally generate suspicious sequences of arbitrary length) But you can't prove that a sequence is indeed random: the sequence [sha256(1), sha256(2), sha256(3), ...] passes the usual tests and isn't even clever. For any set of tests you can write a pseudo random generator that passes them