2 papers
math.NT2004
The 3x+1 Semigroup
David Applegate, Jeffrey C. Lagarias
The 3x+1 semigroup is the multiplicative semigroup generated by the rational numbers of form (2k+1)/(3k+2) for non-negative k, together with 2. This semigroup encodes backward iter…
math.NT2001
Lower bounds for the total stopping time of 3X+1 iterates
David Applegate, Jeffrey C. Lagarias
The 3X+1 function T(n) is (3n+1)/2 if n is odd and n/2 if n is even. The total stopping time σ_\infty (n) for a positive integer n is the number of iterations of the 3x+1 function…