With over 200,000 (named) sequences, this is quite a collection. I’ll feature individual sequences at some point next year, but for now, enjoy this one. A favourite of mine:
The Kolakoski Sequence:
Each symbol occurs in a “run” of either 1 or 2 consecutive terms, and writing down the lengths of these runs gives exactly the same sequence. It is the unique sequence with this property except for the same sequence with the initial 1 deleted.