Redundancy among the three first-tier two-parameter nests

Determine whether the sets of natural numbers a generated by the three first-tier two-parameter nests A, B1, and B2 are redundant with respect to the a-values they provide—i.e., whether one or more of these nests does not yield any a beyond those produced by the others.

Background

The first tier consists of three two-parameter nests derived from specific restrictions in formulations (A) and (B). These nests collectively produce many a-values within N[1000].

The authors explicitly ask whether some of these nests are redundant in terms of the a-values they generate, which would simplify the schema and clarify structural relationships among the nests.