Sequence next in sequence
Jump to navigation
Jump to search
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
Wikipedia page (contains spoilers).