
Between n and (n+1)cycle discs of a
principal series, the smallest cycle number is 2n+1: 
between the 2 and 3 is a 5 
between the 3 and 4 is a 7 
between the 4 and 5 is a 9 

and so on. 

Between consecutive discs whose cycles we have already found, the
smallest cycle number is the sum of those just found. For example, 
between the 2 and 5 is a 7 
between the 5 and 3 is an 8 
between the 3 and 7 is a 10 
between the 7 and 4 is an 11 
between the 4 and 9 is a 13 
between the 9 and 5 is a 14 
between the 5 and 11 is a 16 
between the 11 and 6 is a 17 

and so on. 
This last rule persists to
all levels: between consecutve discs with cycle numbers p and q, the smallest
cycle number is p+q. This arrangement of features is
called the Farey sequence. 