
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I don't run my furnace very much overnight when boondocking - as I like it cool to sleep - so my one battery does good for me even when needing to run the furnace. BUT it does require charging somehow every day (one reason I'd like solar to do that - but now use the genie).
An important factor with your generator - you probably need to have anywhere from 1/4 to 1/2 a tank of gas for the generator to run. That's a safety so you don't run out of gas by running the generator. When I'm planning to boondock for awhile (like at the place in FL I spent a week twice this winter - I make sure to fill up before going there.)