custom electric (110v) timer

I am looking for a timer, much like the kind often used for lamps when you are out of town... set up a timing loop and it cycles power off/on to a device plugged into it. My problem is that all such devices I can find operate on intervals near 1 hour (the quickest I have found has a minimum 15 minute off/on cycle). I need to switch off a device for a few seconds, once each hour or so. My current rough estimate is to go ~59 minutes 40 seconds on, then ~20 seconds off. I may need to tweak that though so something programmable would be great. I am not an electrical pro, but neither am I a stranger to circuits or house wiring. I know all the safety precautions and can solder/assemble components... I would just not be able to come up with my own schematics to create something like this. If anyone is aware of an existing device, I could purchase it... but I would sortof like to DIY it anyway.

110100101108 years ago
555 circuit (there are lots around here) is unreliable at large intervals as hour you have some options make a circuit that closes a relay some seconds after its powered up (normally closed relay in series with big capacitor on dc). combine it with the 15 min timer so it'll reset the relay each hour and the relay comes back after few seconds instead of the timer (for the reset of the relay) you can use a 1/2 hour on - 1/2 hour off clock generated by a 555 and series of clock dividers (T flip flops) set 2 of the 15 min timers with the switch contacts in parallel. set the time in them with 14:40 min skew. set each to 45 min on 15 min off