Classify attractors by similarity

Classify attractors of the shifted Alladi–Erdős map across different shift parameters A into classes whose members are similar.

Background

The shifted Alladi–Erdős map generates a distinct set of nontrivial attractors for each shift parameter A. Although the paper derives line-like relationships among attractor elements as A varies, it does not establish a classification of attractors across different parameter values based on structural similarity.

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"?

— 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

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 $N\to\infty$? Which arithmetic properties distinguish shifts with unusually large residual basin mass or high normalized entropy?

— 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