Lucky Numbers

The lucky numbers are an integer sequence that results from a certain "sieve" process:

Start from the odd natural numbers a = 1 3 5 7 … viewed as a 1-indexed infinite sequence.

For each k = 2…∞, replace a with the result of deleting every a[k]-th term from a.

Print the first 1,000 terms of the resulting sequence.

Start:
    1 3 5 7 9 11 13 15 …
      ^
Delete every 3rd term and advance:
    1 3 7 9 13 15 19 21 …
        ^
Delete every 7th term and advance:
    1 3 7 9 13 15 21 25 …
          ^

External links: OEIS A000959, Rosetta Code, Wikipedia