I picked n=6 in particular because the code checks the past 5 numbers so 6 means that it can't do its frequency analysis but also avoids the problem you mention. And yes, it isn't random, rather it enforces a unique sequence. Because the code looks for repetition one number at a time, a de bruijn sequence has to be pretty optimal since it attempts not to.

Also this sequence seems to work better: 0000001001000101010011010000110010110110001110101110011110111111