My guess is that to a human observer they would seem like a random noise. -- Which contradicts my initial words that the sequence would not be what you'd expect... but I guess the answer is that the generation process is trying to surprise the prediction machine, not me as a human.

"What is the specific pattern of bits?" and "Give a vague description that applies to both this pattern and asymptotically 100% of possible patterns of bits" are very different questions. You're asking the machine the first question and the human the second question, so I'm not surprised the answers are different.