In a numberphile video it is shown why 82000 is an extraordinary number. It can be written using only zeros and ones in base 2, base 3, base 4 and base 5. It is unknown if there are larger numbers for which this is true, and if it can apply to base 6 and higher.
$82000_{10}=10100000001010000_2=11011111001_3=110001100_4=10111000_5$
My question is: is there a similar "special" number that can be written using only zeros and ones in decreasingly negative bases (base -2, base -3, base -4, etc)?
Using python I found that from -100000000 to 100000000 the most negative number that can be written in base -3 and base -4 is $-196335$, the most positive one is $4353$.