The function C is defined on positive integers as follows:

\(C(n) = \begin{cases} \dfrac n 2 & \text{if $n$ is even}, \\ 3n+1 & \text{if $n$ is odd}. \end{cases}\)

Find the smallest positive integer of m such that C^m(9)=1.

Guest Apr 30, 2023

#2**0 **

C^m(x)=C(C(C(C ... (x))))..., performing C m times. Do this to 9:

9 is odd, C(9)=28.

28 is odd, so C(C(9))=14.

14 is even, so C(C(C(9)))=7.

Continue to get 22,11,34,17,52,26,13,40,20,10,5,16,8,4,2,1

After applying C 19 times, we have reached 1. Therefore, the smallest m is **19**.

gb1falcon May 2, 2023