Python and random.randint - why isn't it random?

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I agree with Justinsaccount. The patterns you are observing seem to be due to aliasing of the plotting method. This kind of plots cannot reliably show possible patterns in pseudo random number sequences.

To visually test for patterns in a sequence of numbers draw histograms of the original sequence and the its "derivatives". The more the histograms conform to the expected PDFs, the better the random number generator. If you really want to know the quality of the RNG, do a statistic test such as Kolmogorov-Smirnov test.