r/Collatz•
No_Assist4814

Table mod 16 with color code

The column on the left provides the definition and color code of the main tuples: pairs, triplets and 5-tuples. The table is limited to the classes mod 16 that are involved in tuples, and without 8 and 10 mod 16, the pairs of predecessors.

This table is based on obeservations and preliminary generilizations I made, greatly improved by u/GonzoMath.

It is work in progress. My guess is that some definitions will use subsidiarity, e.g. for preliminary pairs (PP); "PP1: 16k+(2, 3), unless the pair is involved in an odd triplet (OT) or a 5-tuple".

PPs and even triplets (ETs) iterate into lower PPs and ETs. Details will be provided soon.

https://preview.redd.it/oyk972tvnsue1.jpg?width=1600&format=pjpg&auto=webp&s=81213f227ad39637a1b2b90adef9268cb5bde1c4

Posted Apr 14, 2025, 12:44 PM UTC

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