MathDB

The Collaptz function is defined as

C(n) = \begin{cases} 3n - 1 & n\textrm{~odd}, \\ \frac{n}{2} & n\textrm{~even}.\end{cases}

We obtain the Collaptz sequence of a number by repeatedly applying the Collaptz function to that number. For example, the Collaptz sequence of

13

begins with

13, 38, 19, 56, 28, \cdots

and so on. Find the sum of the three smallest positive integers

n

whose Collaptz sequences do not contain

1,

or in other words, do not collaptzse.
Proposed by Andrew Wu and Jason Wang

3