Cron job every three days

Run it every three days...

0 0 */3 * *

How about that?

If you want it to run on specific days of the month, like the 1st, 4th, 7th, etc... then you can just have a conditional in your script that checks for the current day of the month.

if (((date('j') - 1) % 3))
   exit();

or, as @mario points out, you can use date('k') to get the day of the year instead of doing it based on the day of the month.

Because cron is "stateless", it cannot accurately express "frequencies", only "patterns" which it (apparently) continuously matches against the current time.

Rephrasing your question makes this more obvious: "is it possible to run a cronjob at 00:01am every night except skip nights when it had run within 2 nights?" When cron is comparing the current time to job request time patterns, there's no way cron can know if it ran your job in the past.

(it certainly is possible to write a stateful cron that records past jobs and thus includes patterns for matching against this state, but that's not the standard cron included in most operating systems. Such a system would get complicated by requiring the introduction of the concept of when such patterns "reset". For example, is the pattern reset when the time is changed (i.e. the crontab entry is revised)? Look to your favorite calendar app to see how complicated it can get to express Repeating patterns of scheduled events, and note that they don't have the reset problem because the starting calendar event has a natural "start" a/k/a "reset" date. Try rescheduling an every-other-week recurring calendar event to postpone by a week, over christmas for example. Usually you have to terminate that recurring event and restart a completely new one; this illustrates the limited expressivity of how even complicated calendar apps represent repeating patterns. And of course Calendars have a lot of state-- each individual event can be deleted or rescheduled independently [in most calendar apps]).

Further, you probably want to do your job every 3rd night if successful, but if the last one failed, to try again immediately, perhaps the next night (not wait 3 more days) or even sooner, like an hour later (but stop retrying upon morning's arrival). Clearly, cron couldn't possibly know if your job succeeded and the pattern can't also express an alternate more frequent "retry" schedule.

ANYWAY-- You can do what you want yourself. Write a script, tell cron to run it nightly at 00:01am. This script could check the timestamp of something* which records the "last run", and if it was >3 days ago**, perform the job and reset the "last run" timestamp.

(*that timestamped indicator is a bit of persisted state which you can manipulate and examine, but which cron cannot)

**be careful with time arithmetic if you're using human-readable clock time-- twice a year, some days have 23 or 25 hours in their day, and 02:00-02:59 occurs twice in one day or not at all. Use UTC to avoid this.

* * */3 * *  that says, every minute of every hour on every three days. 

0 0 */3 * *  says at 00:00 (midnight) every three days.