A forgotten tuple (with apologies)

Working on 5-tuples, I found a case with two 5-tuples at the same lenght from 1 (not common). As I was preparing the figure, a forgotten tuple emerged. I noticed it in the past, but could not find it when describing formally the tuples. So, here it is, with my apologies:

- An odd-even pair (rosa-blue) iterates into an even triplet (odd-even numbers) in three iterations.

The figure below shows two legitimate 5-tuples, with slighly different features:

- The one on the top uses an odd-even pair instead of an even triplet (fourth iteration); it is easy to check that 912 cannot form a triplet with the odd-even pair.

- The odd-even pair merging into an even triplet "normalizes" the situation.

- The iterations of preliminary pairs into preliminary pairs delay the merges, but in a consistant way.

- The addition of shorter partial sequences before the last merge allows to show the ubiquitous nature of the tuples sometimes hidden in a partial tree.

Partial tree with two 5-tuples

I will now investigate this forgotten tuple and verify where and when it applies.