Here is my sequence (finite):
You just have to figure out its logic.
It is a "sequence" and I like alphabets.
For ADG1, the logic is:
Convert all of the numbers to base 26, and convert each place in each number using A = 1, B = 2, etc. ADG1 then becomes
S, SE, SEQ, SEQU, SEQUE, SEQUEN, SEQUENC, SEQUENCE