Wirth Problem 15.12

December 7, 2012

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.


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