Determine attractor basins analytically

Determine the complete basin of a given attractor of the shifted Alladi–Erdős map by analytic means.

Background

The paper computes basin sizes using finite windows and an algorithm based on prime trees and functional-graph exploration. It does not provide an analytic characterization of all initial values whose trajectories eventually enter a specified attractor.

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?

— 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