  The Collatz problem is related to the fixed point problem, and is widely used
in mathematics. It has attracted a wide range of math enthusiasts, but is still
difficult to solve. So, this article aimed to study the extension of the
Collatz problem, more widely, in k-adic. We define a new sequence called Z
transformation sequence. Under a suitable assumptions, we can prove that the
limit set of the Z transformation sequence must be M={1,2}.
