The next number in the sequence is 1113213211, because the rule for creating the next number is to simply describe the previous number. The first number is 1, or 1 (one) 1, so you get 11. To describe 11, you have two 1's, or 21. Now you have one 2 and one 1, so the next number is 1211. The solution is to simply continue describing the previous number using only numbers.
