Characterize prime-composite patterns in attractors

Characterize the regularity, if any, in the sequences of prime and composite elements occurring in attractor cycles of the shifted Alladi–Erdős map.

Background

Every nontrivial attractor contains prime and composite elements governed respectively by the additive shift and the prime-factor-sum map. The paper identifies line-like parameter dependence but leaves unresolved whether the order or pattern of prime and composite entries in attractor cycles follows a systematic regularity.