Tuples, segments and walls: main features of the Collatz procedure

Based on the observation of the iterative Collatz procedure and its outcome – sequences of numbers forming a tree by their successive merges two by two – we explore in more depth features that are partially known. The main ones are, for any n, a positive integer:

- Three main types of tuples made of consecutive numbers with the same sequence length that merge continuously: pairs, triplets and 5-tuples, with variants.

- The merges generate four types of segments – a partial sequence between two merges – three of them containing two or three numbers.

- Numbers of the form 3p*2m are part of the fourth type of segment. They are infinite and do not merge but once at 3p, creating non-merging walls. A solution to this problem uses series of pseudo-tuples that do not merge in the end.