39942

There are two solutions fot this problem:

1)6,9,11,12,4,14,7
2)8,7,13,10,6,12,9

I tried every combination with the first two digits totalling 15.
Only two out of the 14 sequances provided the correct solution to the problem.
For example:

15 20
1-14 9-11<--A common factor
2-13 8-10
3-12 7-13<--A common factor
4-11
5-10
6-9 <--A common factor
7-8
8-7 <--Also a common factor
9-6
10-5
11-4
12-3
13-2
14-1