Order field values in round-robin in MySQL

I have table like this:

id order_number
 1     20
 2     20
 3     20
 4     21
 5     21 
 6     21
 7     21
 8     21
 9     21
 10    22
 11    23
 12    23
 13    24

I need to arrange the rows such that the order_numbers are arranged round-robin sequence (20,21,22,23,24 then again 20,21,22,23,24 and again 20 etc..), i.e.

id order_number
 1     20
 4     21
 10    22
 11    23
 13    24
 2     20
 5     21
 12    23
 3     20
 6     21
 7     21
 8     21
 9     21

Does anyone know how to write the query for this? Thanks in advance!