Sequence 1, 11, 21

What follows next in the sequence below?

1, 11, 21, 1112, 3112, 211213, 312213, ?


SOLUTION

Every term in the sequence describes how many 1s, 2s, 3s, etc. are there in the previous term. "11" means that in the previous term there is one 1. "21" means that in the previous term there are two 1s. "1112" means that in the previous term there is one 1 and one 2. "3112" means that in the previous term there are three 1s and one 2. "211213" means that in the previous term there are two 1s, one 2 and one 3. "312213" means that in the previous term there are three 1s, two 2s and one 3. Therefore the next number in the sequence should be 212223.