For those not ready to switch from celebrating regular birthdays every year to celebrating binaversaries every power-of-two years, you can still save on candles by basing them on binary code. There seem to be some variants out there, but the one I like best is that suggested at halfbakery or used by a touch of grey, which is to put in a candle for each binary digit you want, and then just light those that correspond to binary one.

For binaversaries, you just use regular candles. Running out of space for candles is not likely to happen to you in your lifetime, unless you live to something like 65536 years (16 byears). So that's one less problem...