Under the unproven Weak Residue Conjecture, the paper derives six logarithm formulas linking total, odd, and even step counts of a Collatz trajectory, one of which is equivalent to the conjecture itself.
Ladue, Clusters of Integers With Equal Total Stopping Times in the 3X + 1 Problem, Fibonacci Quart, 56(2):156-162, 2018
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Iteration Steps of 3x+1 Problem
Under the unproven Weak Residue Conjecture, the paper derives six logarithm formulas linking total, odd, and even step counts of a Collatz trajectory, one of which is equivalent to the conjecture itself.