A conjugate Collatz map is conjectured to partition N\{1} into strings running from 2 mod 3 to 3 mod 4, which would imply every nontrivial Collatz trajectory hits a number 5 mod 8.
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The 3n+1 problem: a partition of interest
A conjugate Collatz map is conjectured to partition N\{1} into strings running from 2 mod 3 to 3 mod 4, which would imply every nontrivial Collatz trajectory hits a number 5 mod 8.