# ><>, 25 bytes, depth 2, A001333 from A002522
    301-v >rn;
    *2@:<r^!?:-1r+

These are the numerators of the continued fraction convergents to sqrt(2).
The code needs the user to prepopulate the stack with the index of the convergent that should be returned. Indexing starts at 1. 
The next answer should start with the terms:

    1, 1