Finding groups within time series in Postgre

I have a list of timestamps and i want to tag them as a group when they are close enough (less than 15 sec intervall). This is what I want to have eventually :

time	group number
18:01:00	1
18:01:06	1
18:10:00	/
18:20:30	2
18:20:40	2
18:20:50	2
18:25:02	/

Answer

Use lag() and date comparisons to determine where a group begins. Then use a cumulative sum. You actually only want to include rows that have multiple rows in the group, so this is a little tricker than the simple gaps-and-islands problem:

select t.*,
       (case when prev_time > time - interval '15 second' or
                  next_time < time + interval '15 second'
             then sum(case when prev_time > time - interval '15 sec' then 0 else 1 end) over (order by time)
        end) as group_number
  from (select t.*,
               lag(time) over (order by time) as prev_time,
               lead(time) over (order by time) as next_time
        from t
       ) t