A Variant Explored

The Prompt

Design and explore a variant of the Collatz process — change the multiplier from 3 to 5 or 7, alter the additive constant, extend to negative integers, or work in a different number base. Compute trajectories for at least twenty starting values. Record any cycles, divergent behaviour, or unexpected regularities, and compare the variant's dynamics to the classical 3n + 1 map.

Completion Criteria

A written specification of the variant, a table or chart of trajectories for at least twenty starting values, and a one-paragraph comparison to the classical conjecture.

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