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).