My friend was asked this question at a job interview (it was nothing math related, so I assume it was more of a "let's see how you think" kind of question, not "how well can you identify series") and, naturally, being the math person he asked me.
That said, I have no idea what this sequence is so I decided to ask you guys. I'm relatively new to this site so I apologize if this is off-topic with the posts that are usually here.
The next number in the sequence is $88979$.
I see that the numbers involved are strictly increasing and that they do not differ by more than two, so I suspect this has to do with base $3$ where, in each successive term, the digits are increased by $1$ (the first term being $\{0, 1, 2\}$, then the next term the digits are $\{1, 2, 3\}$, etc.). So I deciphered this "code" to get, in base $3$: $1, 2, 11, 22, 121, 1012, 2101$. In decimal, these are $1, 2, 4, 8, 16, 32, 64$ -- powers of two.
So, the next term should be $128$ in base $3$, where $\{0, 1, 2\} \rightarrow \{7, 8, 9\}$ This gives an answer of $11202 \rightarrow 88979$.