Unifying the scale for pairs and triplets
It is a follow-up to [Calculations of the scale of tuples with k=0 : r/Collatz](https://www.reddit.com/r/Collatz/comments/1khi70u/calculations_of_the_scale_of_tuples_with_k0/).
It is an attempt to put together bits and pieces about even triplets and even pairs, using the figure below:
- The scale mentioned in the post above holds. Even triplets and pairs operate by groups of four, except the lowest one that deals with the trivial cycle.
- As an example, the partial tree obtained for 28-30 +128k (yellow) with k=0 is detailed. It shows the characteristics of the isolation mechanism* - with the even numbers aligned on the right.
- It interacts with the converging series of preliminary pairs with the same k. One can see that this series fits the top of the yellow part. I verified several cases
|| || |p| | |k| | | | |8|1|11|101|911|8201|73811| |16|2|20|182|1640|14762|132860| |24|3|29|263|2369|21323|191909| |32|4|38|344|3098|27884|250958| |40|5|47|425|3827|34445|310007 |
* [Overview of the project (structured presentation of the posts with comments) : r/Collatz](https://www.reddit.com/r/Collatz/comments/1k98c5a/overview_of_the_project_structured_presentation/)
Posted May 8, 2025, 7:59 AM UTC
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