Old Puzzler

Does anyone remember a puzzler like this and can they help me with getting it right?:
There was an old Cartalk puzzle I heard back around 1993 or 1994 or thereabouts. It goes something like this: You have the following number sequence:
1,11,21,1211,… and you ask what the next number in the sequence is. I can’t quite remember what the answer is, but I think it’s something along the line of each succeeding number in the sequence describes the number preceding it. For example, just starting with “1”, the number following it is 1 of the digit “1”, so that succeeding number becomes 1 (of) 1, or 11. The next number describes the preceding number as the quantity 2 of digits “1”, so that next number becomes 2 (of) 1, or 21. The next number describes the preceding number as 1 of the digit “2” and 1 of the digit “1”, so that becomes 1 (of) 2 and 1 (of) “1”, or just 1211. In this case, I think the following number in the series describes the preceding number as 1 of 1, 1 of 2 and 2 of 1, or 111221. I’m not grouping the numbers together, but simply reading them from left to right as individual digits, but I am grouping the consecutive repeated digits together. I’m probably not making total sense here, but if you can find that puzzle somewhere in your archives, that would help me. And obviously I should be doing something better with my time. Nonetheless, can you help me here?
I’m a big fan of both Cartalk and public radio! I’m so sorry to hear of Tom’s passing away. He was a great guy.

My head hurts. Maybe it’ll be in the re-runs.

Well-known sequence:

Don’t worry @ahclem42, even if the answer given by insightful for today’s puzzle is correct, and you submit it, I don’t think they are giving out new prizes. The show is all reruns now.

@ahclem42, we are still accepting puzzler responses through cartalk.com and we do encourage you to submit! A winner is still selected weekly.