1
11
21
1211
111221
312211
13112221
1113213211
31131211131221
13211311123113112211
11131221133112132113212221
3113112221232112111312211312113211
1321132132111213122112311311222113111221131221
etc.
The way this sequence works is described in 1, 11, 21, 1211.
Things that are interesting to prove about this sequence, in order of difficulty:
- There will never be a 4, or anything higher, in this sequence.
- If the sequence started with 2 instead of 1, every number after the 2nd would end with '112'.
- The sequence will never get shorter.
- If you consider a new sequence, comprised of digits m through n of each step, this sequence will eventually cycle. (For example, this sequence where m=1 and n=2 is 11, 21, 12, 11, 31, 13, 11, 31, 13 ...)