?? This does not clarify -- your initial post made a claim about 0^2, which (correctly) does not appear in this list. Moreover it is trivial that there are no

?? This does not clarify -- your initial post made a claim about 0^2, which (correctly) does not appear in this list. Moreover it is trivial that there are no negative powers of 2 that have all even digits, since the trailing digit will always be 5. So the question reduces to whether there are powers of 2 greater than 2048 that have all even digits.