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.
The 3x+1 Problem: An Annotated Bibliography, II (2000-2009)
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abstract
The 3x+1 problem concerns iteration of the map T(n) =(3n+1)/2 if n odd; n/2 if n even. The 3x +1 Conjecture asserts that for every positive integer n>1 the forward orbit of n includes the integer 1. This paper is an annotated bibliography of work done on the 3x+1 problem published from 2000 through 2009, plus some later papers that were preprints by 2009. This is a sequel to an annotated bibliography on the 3x+1 problem covering 1963-1999. At present the 3x+1 Conjecture remains unsolved.
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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.