- #1

elcaro

- 128

- 28

- TL;DR Summary
- Expanding the Collatz sequence by replacing 3n+1 with 3n+2k+1 for k=0,1,2,...

For k=0 we get the original sequence, leading to the cycle 4-2-1. If the Collatz conjecture holds, that would be true for all integer values of n>0.

For values of k>0 we get different cycles.

For k=1 we for instance get the cycle 3-12-6-3

What we want to investigate is:

- What cycle is the sequence iterating to for different values of k?

- Is that cycle unique for k (independent of the seed number)?

Has this expanded Collatz sequence been explored previously?