The \(3x+1\) problem as a string rewriting system
Let \(T^k(n)\) be the value after \(k\) iterations in the \(3x+1\) problem. The author reformulates the conjecture in two assertions: (I) Every odd \(n\) lies on a distinct \(3x+1\) trajectory between two Mersenne numbers \(2^k-1\) or their equivalents; (II) If \(T^r(2^k-1)\to 2^l-1\) for any \(r,k,l>0\) then \(l<k\).
scientific article; zbMATH DE number 5847817
scientific article