This record addresses Bala’s conjecture (vii) for OEIS A006165 by describing both the iterates of the sequence and its complete inverse images.
What the record establishes
The manuscript classifies the forward orbits and identifies which integers map to the same value, separating the cases in which repetitions occur. It turns the conjectural description into an explicit proof record.
Public materials
View the public record and manuscript on Zenodo ↗
Current external status
The manuscript and supporting material are public on Zenodo. An email requesting review was rejected by the recipient’s mail server, and no OEIS update, independent expert review, or acceptance has yet been confirmed.