Computational study reveals convergence dependence on block length in a Collatz-type map, suggesting unique cycles.
We study a Collatz-type map in which the odd-step alternates between 3n + 1 and 3n − 1. Computations up to 107 show that convergence depends strongly on the block length L, with a singular behavior at L = 2, where approximately half of the initial values enter a unique 44-cycle.
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Masanori Fujii (2026) studied this question.
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