Puzzle of the Week #290 - Special Sequence

This is a special sequence:

3 1 2 1 3 2

For each number ‘k’ from 1 to 3, the number of numbers between the pair of ‘k’s is equal to k.

In other words, there is one number between the pair of 1s, two numbers between the pair of 2s and three numbers between the pair of 3s.

Can you create a similar sequence containing pairs of numbers but using numbers 4, 5, 6 etc up to n (n can be whatever you need it to be to make a sequence that has no gaps), where for each number k, the number of numbers between the pair of ‘k’s is k (so there will be four numbers between the pairs of 4s, five numbers between the pair of 5s, etc.)?