Just a guess: each term describes the number of times each digit appears in the previous term, with the exception of the first term, which is defined as 1?

1
11 (one one)
21 (two ones)
1211 (one two, one one)
111221 (one one, one two, two ones)
...
Interestingly, I don't think it is possible to ever get a four to appear here. Does that sound right?

Originally posted by royalchicken Just a guess: each term describes the number of times each digit appears in the previous term, with the exception of the first term, which is defined as 1?

1
11 (one one)
21 (two ones)
1211 (one two, one one)
111221 (one one, one two, two ones)
...
Interestingly, I don't think it is possible to ever get a four to appear here. Does that sound right?

Hmm, too easy ðŸ˜‰
I don't know about a four coming up, but looking at the other posts, it doesn't seem that it'll appear in a row.

In fact, note that any three digit sequence in a term becomes a two digit one in the next term, two digits ones become two-digit ones, and one digits ones become one-digit ones. So if you know the relative frequencies of one-, two-, and three-digit blocks you can find an easy asymptotic estimate of the number of digits in the nth term...any guesses here? I'll tell you if you're right...