View source for 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==

{{Hint| Count the number of repeating digits.}}

{{Answer| 2}}

{{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==

[https://en.wikipedia.org/wiki/Kolakoski_sequence Wikipedia page] (contains spoilers).

[[Category:Short puzzles]]
[[Category:Sequences]]

__NOTOC__