r/Collatz•
No_Assist4814

Tuples or not tuple ?

The following example intends to help readers identifying tuples:

Definition (Tuple): A tuple is a set of consecutive numbers with the same sequence length that merge continuously (roughly: a change occurs at most every third iteration*)

  1. All sequences have the same lenght.

  2. All sequences merge.

  3. There are several groups of consecutive numbers: 98-102, 642-643, 652-653, 662-663.

  4. All final pairs (orange-yellow) merge in three iterations.

  5. All preliminary pairs (green-red) iterate into another preliminary pair or a final pair in two iterations.

  6. The 5-tuple, even triplet (orange-yellow, light blue) and odd triplet (rosa-green-red) see their pairs behave as like the other pairs; the singletons follow suite.

  7. The 5-tuple and pairs identify in point 3 are validated. Each of these tuples merge with the others in a dicontinuous way.

https://preview.redd.it/az8apkxb3jte1.jpg?width=922&format=pjpg&auto=webp&s=90a3622fadc3787b1bb31ff150e951243fac87bc

Posted Apr 8, 2025, 3:35 AM UTC

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