$3n+3^k$: New Perspective on Collatz Conjecture

Naouel Boulkaboul

Collatz conjecture is generalized to $3n+3^k$ ($k\in N$). Operating as usual, every sequence seems to reach $3^k$ and end up in the loop $3^k,4.3^k,2.3^k,3^k$. The usual $3n+1$ c…