Sequence next in sequence

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

Puzzle

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

Help

Hint
Answer
Solution

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).