The work is devoted to the study of dynamical systems with point attractors by the recurrent method of transforming discrete data from the set of natural numbers, in the direction of increasing powers of two (direct Jacobsthal problem) and in the opposite direction (reverse Collatz problem). The idea of splitting the set N into separate non-overlapping subsets by Jacobsthal transformation of numbers was also expressed for the first time. It was established that this effect correlates with the regularities of Collatz-type sequences in the reverse direction of the transformation of the set N of initial numbers. It is shown that the number of segregation groups of the set N correlates with the number of periodic cycles of completion of Collatz sequences, plus the group of numbers that forms infinitely increasing Collatz sequences.
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