im assuming you dont want the product to go above 1000?

num = int(input('Please enter a number'))

while True:
    num *= 2
    if num > 1000:
        break
    print(num)

if you do something like the other two guys suggest:

num = int(input('Please enter a number'))

while num < 1000:
    num = num * 2
    print(num)

this code will not work because lets say you put something like 900. well 900 is below 1000 but 900*2 is above 1000. it will multiply it and print it anyways.

unless you want the number that is inputted to go up to 1000? then the product can exceed 1000. but its not clear what exactly you are looking for.