Here's some more:
1 ;1
11 ;2
21 ;2
1211 ;4
111221 ;6
312211 ;6
13112221 ;8
1113213211 ;10
31131211131221 ;14
13211311123113112211 ;16
11131221133112132113212221 ;22
3113112221232112111312211312113211 ;30
1321132132111213122112311311222113111221131221 ;42
The sequence on the right is the amount of digits in each row. Can anyone fit a formula to that series?
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 royalchickenHmm, too easy 😉
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?
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...