Collatz Sequence: Negative Parity Invariance, Saturation Point, and Cycles

In this paper, we consider the Collatz sequence, i.e., the discrete 3n+1 or the (3n+1)/2 sequence, where it is known that the presence of at least one cycle is guaranteed, given by (1421) and (121), respectively. The above sequence is noted to lack parity invariance, and the new related sequence has no saturation point.