And the more I think about this one the more I wonder if something bigger is wrong. It just is not normal to kill light bulbs because of 1k watt miner assuming decent wiring, and breaker is decent. LED likely will be a fix... but I wonder underlining cause.
Honestly you might think about getting a electrician even if the LED fixes it. I would ask them to check gauge of wire, make sure it still seems to be of ok quality and no issues. Really open up the breaker box and look at what's behind the metal front (I dont suggest doing this on your own if not use to electricity and don't have power to house off. The main can be a scary thing on amount of electricity).
You can run some things yourself like checking circuit - http://www.amazon.com/Sperry-Instruments-GFI6302-Outlet-Tester/dp/B000RUL2UU/ . That is kinda a DIY version a electrician will be much better on that.
Honestly it highly likely is my wiring / electrical setup, this house is very old and I don't think the electric systems have been looked at for a very long time.