What number comes next?

[magenta321]

What row of numbers comes next?

1
11
21
1211
111221
312211
13112221

[jenninca]

1113213211

Woo-hoo! I figured it out!

[magenta321]

Cindy is right, she figured it out.

Now does anyone want to tackle why that is correct?

[hymie[$]]

This is another oldie. Each successor counts the runs of digits in the predecessor.

1 has one 1, hence 11
11 has two 1s, hence 21
21 has one 2 and one 1, hence 1211
1211 has one 1, one 2, and 2 1s, hence 111221
and so on

[magenta321]

Well done Hymie and Cindy!!!

[hymie[$]]

By the way, if you ever need to solve something like this, there's the On-Line Encyclopedia of Integer Sequences at http://www.research.att.com/~njas/sequences/index.html.
It readily identifies this sequence (but I didn't use it to find my answer!)