The Modified Collatz Conjecture

The Collatz Conjecture is a sequence conjecture that is defined as follows:

Start with a positive integer $n$ . If $n$ is even, then divide it by two. If $n$ is odd, then multiply it by three and add it with one. Repeat this with the remaining term. For all positive integers $n$ , this sequence will always reach 1.

For example, we choose the number 3. Then the sequence is

3 , 10 , 5 , 16 , 8 , 4 , 2 , 1

This time, we have the Modified Collatz Conjecture that is defined as follows:

Start with a positive integer $n$ . If $n$ is even, then divide it by two. If $n$ is odd, then multiply it by three and subtract it by one. Repeat this with the remaining term. For all positive integers $n$ , this sequence will always reach 1.

For example, we choose the number 3. Then the sequence is:

3 , 8 , 4 , 2 , 1

We can call the number 3 a "proving number" of the Modified Collatz Conjecture because the number 3 makes this conjecture true . The opposite of the proving number is "disproving number". A number $x$ is a "disproving number" of this conjecture if the number $x$ makes this conjecture false .

Which of the following statement is true?