MathDB

Let

y_{1}, y_{2}, y_{3},\ldots

be a sequence such that

y_{1}=1

and, for

k>0,

is defined by the relationship:

y_{2k}=\begin{cases}2y_{k}& \text{if}~k~ \text{is even}\\ 2y_{k}+1 & \text{if}~k~ \text{is odd}\end{cases}

y_{2k+1}=\begin{cases}2y_{k}& \text{if}~k~ \text{is odd}\\ 2y_{k}+1 & \text{if}~k~ \text{is even}\end{cases}

Show that the sequence takes on every positive integer value exactly once.

Problem Statement