What is next in this sequence of numbers: 1, 11, 21, 1211, 111221, 312211, ... ?

13112221

Step-by-step explanation:

Each sequence of numbers is a verbal representation of the sequence before it. Thus, starting with 1, the next sequence would be "one one," or "11." That sequence is followed by "two one," or "21," and so on and so forth.

This may also be a good explanation:

The first number is just ONE (amount) "1" (0-9 numeral). So if you say there's ONE "1" (seriously just say it aloud) the next number would be an 11. Then there are TWO "1's", creating 21. Then ONE "2" and ONE "1" which creates 1,211. Then ONE "1", ONE "2", and TWO "1's" creating 111,221 ... and so on.

The first number 1 is read as one one, so the second number is written as 11, this is read as two ones, so the next number is written as 21 (two ones)

This continues throughout the sequence.

The last number written is 312211 which is read as one three, one one, two twos, two ones

This gets written as 13112221