I have a logging application that should produce an entry in the
database every minute or so, give or take a few seconds.

I'm interested in finding out
a: what minutes don't have a record and
b: periods where the gap exceeded a certain amount of time.

Is this not the same question ?

        Answer to a:

If your script is set to run at every minute + 00 seconds, if it ever runs one second earlier, timestamp-truncate will keep the previous minute and you're screwed. A simple solution would be to have your script run every minute + 30 seconds.

        Answer to b:

If you can do the following : examine the records in chronological order, every time computing the delay between record N and record N-1 ; if this delay is not one minute +/- a few seconds, you have detected an anomaly.
Problem : you need to scan the whole table for anomalies every time.
Solution : put an ON INSERT trigger on your log table which :
- checks the current time for sanity (ie. is it +/- a few seconds from the expected time ?)
This solves part of a)
- looks at the timestamp of the latest row, computes the difference with the inserted one, and if > than 1 minute + a few seconds, inserts a row in an anomaly logging table.
This solves the rest of a) and b)


It's just an additional SELECT x FROM table ORDER BY timestamp DESC LIMIT 1 which has a negligible performance impact compared to your insert.

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TIP 9: the planner will ignore your desire to choose an index scan if your
     joining column's datatypes do not match

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