I want to know what each number would be in a different base, upon input. Quickly.
I remember hearing my first base 2 joke in Junior High. Then in High School we talked about base 3, and how it was likely that the critters in the then-hit remake of 'War of the Worlds' probably used it.
That genuine curiosity about numbers led me to develop a simple one page application that would allow the user to input a base 10 figure and translate what it would be in other bases. Fun!