#codingexercise
Generate n numbers in ascending orders which are having given k factors.
For example, if we are given {2,3,4,7}
The numbers generated would be 2,3,4,6,7,8,9,10...
Let us assume that there are no duplicates in the number.

# http://www.cs.utexas.edu/users/EWD/ewd07xx/EWD792.PDF

n = 15

bases = [2, 3, 4, 7]

nums = [1] * n

candidates_indexes = [0 for _ in bases]

candidates = [base for base in bases]

for i in range(1, n):

    nextn = min(candidates)

    nums[i] = nextn

    for index, val in enumerate(candidates):

        if val == nextn:

            candidates_indexes[index] += 1

            candidates[index] = bases[index] * nums[candidates_indexes[index]]

print(nums)
Start:
candidates=[]

candidate_indexes []
nums[2]

From Stackoverflow
The original design talked about prime factors. Here we have liberally used non primes.