Question 91
Determine if there exists an infinite sequence of positive integers
$$
a_{1}, a_{2}, a_{3}, \ldots
$$
such that
(i) each positive integer occurs exactly once in the sequence, and
(ii) each positive integer occurs exactly once in the sequence $\left|a_{1}-a_{2}\right|, \left|a_{2}-a_{3}\right|, \ldots, \left|a_{k}-a_{k+1}\right|, \ldots$
$$
a_{1}, a_{2}, a_{3}, \ldots
$$
such that
(i) each positive integer occurs exactly once in the sequence, and
(ii) each positive integer occurs exactly once in the sequence $\left|a_{1}-a_{2}\right|, \left|a_{2}-a_{3}\right|, \ldots, \left|a_{k}-a_{k+1}\right|, \ldots$