Just to make clear I understood the problem statement, please confirm or correct the following statements:

- only addition is allowed, i.e. one can't subtract or similar

- the order of the digits must me observed, i.e. it is not allowed to convert 6724 to 62 + 7 + 4, for example

These are the S-Numbers my algorithm found: 81, 1296, 2025, 3025, 6724, 8281, 9801. Which am I missing? (I don't consider them spoilers, as they don't reveal anything about the algorithm, but if they are, feel free to remove them)