In his 1973 book Systematic Programming: An Introduction, Niklaus Wirth gives the following problem as exercise 15.12:
Develop a program that generates in ascending order the least 100 numbers of the set M, where M is defined as follows:
a) The number 1 is in M.
b) If x is in M, then y = 2 * x + 1 and z = 3 * x + 1 are also in M.
c) No other numbers are in M.
Wirth also gives the first six numbers in the result sequence: 1, 3, 4, 7, 9, 10….
Your task is to write a program that finds the first n numbers in Wirth’s sequence, and use it to solve Wirth’s exercise. When you are finished, you are welcome to read or run a suggested solution, or to post your own solution or discuss the exercise in the comments below.