Sequence next in sequence

This sequence guessing puzzle hides a beautiful, well known sequence.

Puzzle

What comes next: 1, 2, 2, 1, 1, 2, 1, ....?

Help

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Hint

Count the number of repeating digits.

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Answer

2

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Solution

This is the famous Kolakoski sequence (see the wikipedia page listed below). The sequence self-encodes the run length of repeated digits. These run lengths are 1, 2, 2, 1, 1, 2, 1,...., which is the sequence again.

Bonus

Find a sequence using the numbers 1, 2, and 3 that has the same property as the one above.

References

Wikipedia page (contains spoilers).