Disjoint tuples in blue-green even triplets and preliminary series
As I am preparing a new update of the overview of the project, I will post stuff that I need but cannot be related directly to recent work.
Here, I extend the disjoint tuples notion to the other type of series.
It does not go very far, as they are based on two-numbers segments and does not have the same "cascade effect" of the 5-tuples/keytuples series, based on three.numbers segments.
The disjoint tuples are of the form of the triplet 2n, 2n+1 and 2n+2 and the odd singleton 2n+3.
I allow myself to repeat that these cases are the only ones in which a quick increase in values is possible and that the triangle is infinite, but the series grow slowly.
[Updated overview of the project (structured presentation of the posts with comments) : r/Collatz](https://www.reddit.com/r/Collatz/comments/1mf41d3/updated_overview_of_the_project_structured/)
Posted Nov 9, 2025, 6:07 PM UTC