While working on algorithmic solutions for finding loops in the standard 3x+1 equation I noticed that some of the "not quite" solutions predicted 4-cycles and 7-cycles in the 3x+47 equation. These are cycles of odd numbers. When I drew out the networks I also found a cycle of 16 odd numbers, and 47 generates it's own 1-cycle (as 3 x 47 + 47 = 4 x 47). These cycles are shown in the following illustration, which includes all the odd numbers up to 101.
(c) John Whitehouse 2011 - 2017