  Note that the restriction to effective properties of sequences is crucial here. If we allowed, for example, the property being identical to my favourite random sequence x, that would define a test which the sequence \(x\) would fail, even though it is random. But it follows from our observations about von Mises randomness (which is still a necessary condition on randomness) that no effectively computable sequence is random (if it were, there would be a place selection definable from the algorithm that selected all the 1s in the sequence). So there is no effective test that checks whether a given sequence is identical to some random sequence.