$ cat -n file
1 col1 col2 col3 col4 col5 14
2 col1 col2 col3 col4 col5 15
3 col1 col2 col3 col4 col5 16
4 col1 col2 col3 col4 col5 1
5 col1 col2 col3 col4 col5 2
6 col1 col2 col3 col4 col5 15
7 col1 col2 col3 col4 col5 16
8 col1 col2 col3 col4 col5 4
9 col1 col2 col3 col4 col5 5
$ awk '{if (p % 16 + 1 != $6) printf("line %d is bad: %s\n", NR, $0); p=$6}' file
line 1 is bad: col1 col2 col3 col4 col5 14
line 6 is bad: col1 col2 col3 col4 col5 15
line 8 is bad: col1 col2 col3 col4 col5 4
Para entender o valor do operador de módulo "%" (divisão restante), você pode brincar com este snippet awk:
$ yes | head -n 40 | awk '{x=NR-1; print x, "->", x % 16}'
0 -> 0
1 -> 1
2 -> 2
[...]
14 -> 14
15 -> 15
16 -> 0
17 -> 1
18 -> 2
[...]