r/Collatz•
No_Assist4814

How classes of preliminary pairs iterate into the lower class, with the help of triplets and 5-tuples

This is the result of work in progress with u/GonzoMath. In a comment, (s)he came out with the following extension of the preliminary pairs (PPx).

FP (=PP0): 8k+(4, 5)
PP1: 16k+(2, 3)
PP2: 32k+(22, 23)
PP3: 64k+(14, 15)
PP4: 128k+(94, 95)
PP5: 256k+(62, 63)
PP6: 512k+(382, 383)
PP7: 1024k+(254, 255)

Moreover, these PPs iterate to the lower level. Triplets and 5-tuples get involved, like in the example below. The color cade used is consistent with the list above. At the bottom, the succession of colors is perhaps easier to follow.

Triplets are not differentiated at this stage.

https://preview.redd.it/cbgq7xj841ue1.jpg?width=1600&format=pjpg&auto=webp&s=198f4ac2282dbbf2a3e54c102174130077b2dae6

Posted Apr 10, 2025, 3:54 PM UTC

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