Another interesting sequence of numbers is produced by starting out with the list of all integers 1, 2, 3, ..., n. From this list every second number is removed to produce a new list. From the new list every third number is removed to give yet another list. Every fourth number is removed from this list and so the process continues. The numbers that remain after this process are called the lucky numbers. The first seven lucky numbers are 1, 3, 7, 9, 13, 15, 21,... . Design an algorithm to list the lucky numbers in the first n integers.