Disjoint odd triplets
Odd triplets are of the form (2p+1. 2p+2, 2p+3) and are present in the tree in different forms (see figure below):
- Continuous odd triplets iterate from 5-tuples and merge continuously (usual colors).
- Disjoint odd triplets have a first odd number as a singleton, while the two other numbers, at the same distance from 1, form at least a consecutive pair that merges continuously, visible in the figure (all orange).
- Some odd triplets have a first odd number as a singleton, while the two other numbers form at least a consecutive pair that merges continuously, present in other parts of the tree, not visible in the figure (dark blue).
- Other odd triplets with three singletons (red).
I intend to further investigate disjoint odd triplets. They contribute to explain Gao (1993) findings.
[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 Oct 25, 2025, 10:57 AM UTC
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