3x + 1
Problem and its Generalizations
Jeffrey C. Lagarias
AT&T Bell Laboratories
Murray Hill, NJ 07974
(January 16, 1996)
A list of
A linked list of keywords
The 3x+1 problem.
A heuristic argument.
Behavior of the stopping time function.
What is the relation between the coefficient stopping time and the stopping time?
How many elements don't have a finite stopping time?
Behavior of the total stopping time function.
Are there non-trivial cycles?
Do divergent trajectories exist?
Connections of the problem to ergodic theory.
Generalizations of problem.
Algorithmic decidability questions.
Existence of stopping times for almost all integers.
Fractional parts of (3/2)^k.
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