The 3x+ 1 Conjecture asserts that the T -orbit of every positive integer contains 1, where T maps x 7→ x/2 for x even and x 7→ (3x + 1)/2 for x odd. A set S of positive integers is sufficient if the orbit of each positive integer intersects the orbit of some member of S. In [9] it was shown that every arithmetic sequence is sufficient. In this paper we further investigate the concept of suffici...
