Once you determine what the rule entails, discovering the next term is very easy. Each number is determined exclusively by the previous number, by the way, but not in the standard mathematical way.

Originally posted by brobluto I think so, but I'm struggling with when the number 4 will occur in the series... (I don't think it will)

In order to get a 4, you would need either 1,2,or3 repeated 4 times:

1111
2222
3333

This would require a break from the sequence so I don't believe the number 4 is achievable. Is that correct?

I believe you are correct that the number 4 will never appear. since each 'description' is two digits long, and the second digit is the character that appeared, you will never have two descriptions in a row with the same second character.