**
Solution :**

Put . Suppose that first n terms of the required permutation are already constructed and m is the minimal natural number which does not belong to the set and M is the maximal natural number which belongs to the set .

Notation: . We put , , where the natural number t is chosen such that . Now note that is divisible by , and is divisible by . By construction each natural number will be included (only once) into constructed sequence.