\begin{definition}[Definition:Lucky Number]
Start with the list of (strictly) positive integers:
:$1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, \ldots$
Remove every $2$nd number from $2$ onwards (that is, all the even integers):
:$1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, \ldots$
The $2$nd term is $3$. Starting from the $3$rd element in this list (which is $5$), remove every $3$rd element from what is left:
:$1, 3, 7, 9, 13, 15, 19, 21, 25, \ldots$
The $3$rd number is now $7$. Starting from the $7$th element in this list (which is $19$), remove every $7$th element from what is left:
:$1, 3, 7, 9, 13, 15, 21, 25, \ldots$
The numbers remaining are the '''lucky numbers'''.
\end{definition}