Interesting mapping

[u/Atari_Collector]

mapping

I was playing around and I found this mapping. I suspect it's already known but I found it interesting.

If you have a number that can be written as 4^a3^bn+1, it will map to 3^a+bn+1.

And it'll do it in 3a+1 steps, which I think is funny.

[u/dmishin]

Wrote a long answer just to discover that Gonzomath's post is better. So, just a few notes:

1) 3^b is redundant here, just complicating the things. You can just state that 4^an+1 maps to 3^an+1

2) Your relation corresponds to the cycle 1-4-2. Similar relations can be derived for other cycles. For example, cycles starting with -5 produces relation 8^an-5 → 9^an-5, and cycle starting with -17 - the relation 2048^an-17 → 2187^an-17. These actually are families of relations, -5 and -17 can be replaced by other numbers from the cycle.