Establish infinite-window basin-size limits

Establish whether the basin sizes of attractors of the shifted Alladi–Erdős map stabilize as the initial-condition cutoff N tends to infinity for a fixed shift parameter A.

Background

Basin fractions in the paper are measured over the finite window 2 ≤ n ≤ N. The numerical appendix reports that basin fractions converge more slowly as N grows because additional levels of the prime trees are included, but the existence of limiting basin sizes for fixed A is not established.

References

The work opens several questions. Can attractors corresponding to different values of $A$ be grouped into classes so that attractors in a given class are ``similar"? Is there a regularity in the sequence of primes and composites in these attractors? Is it possible to identify the complete basin of a given attractor analytically? For a fixed $A$, do basin sizes stabilize in the limit $N\to\infty$?

— Attractors and basins generated by repeated sums of prime factors of natural numbers  (2609.29232 - Shekatkar et al., 24 Sep 2026) in Section Discussion and conclusions