Checking noise in binary sequence for randomness

I have a data set that is made up of a binary sequence, e.g.

0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, ...

the probability of 0 and 1 (noise) is different with 1 being less frequent. I want to know if these 1s happens in groups or they are really just random. How can I tell?

If I feed it into randomness test, it will sure tell me the sequence are heavily gravitating toward 0. Would measuring the gap between 1s be a good test? I am most familiar with Python and C.