The next number in this series will be: 13112221. Here each number tells the story of how previous number was formed. Each number tells you about the occurence of each digit in a number.
Explanation: First number is 1. This number has just 1 “1”, so the next number becomes 11. Now, this number has 2 “1”‘s, so the next number is 21. Then, this number has 1 “2” and 1 “1”, so the next number becomes 1211. This number has 1″1″, then 1 “2” and 2 “1”‘s, so the next number becomes 111221 and so on.

This sequence is based on Run Length Encoding: https://en.wikipedia.org/wiki/Run-length_encoding