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You are still choosing random numbers here. The Kolakoski sequence has zero randomness whatsoever.

Do we care similarly about the version of this that starts on 2?

2, 2, 1, 1, 2, 1, 2...

2, 2, 1, 1,

Again no randomness. Just a variant of the above and trivial to continue this.

This is just the Kolakoski sequence starting from the second term.

Ahh that makes sense. Thank you!