 #1
elcaro
 116
 25
 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 421. 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 31263
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?