for your reply. However while it certainly added to my understanding of the topic, your method yielded no solution for any number that I pulled randomly out of the air, such as 341, 724, 651, 873 (like your example of 125). No doubt I'd have eventually hit on one, but it leads to the questions: what proportion of 3-digit numbers are decomposable this way, and is there a way of knowing in advance?
Interesting that my example 685 has three reversible components (not four as you say unless I've left something out), but applying your formula to it also yields 689 and 788 for k = 7 and 9. These are the two the 3-digit Lychrel (candidate) seed numbers, which I'm also interested in.
Also 651/2 = 325.5, which reversed and added a couple of times gives 651.156, which could be regarded as a fair approximation, would you say? Maybe that's the beginning of an alternative method.