The sum of a run of odd numbers starting from 1 is a perfect square, and you can use this to get the sequence of all perfect squares. ex. 1 = 12, 1 + 3 = 4 = 22, 1 + 3 + 5 = 9 = 32, and so on.
This is a computer fact because it was used in the original Macintosh, which ran on a Motorola 68000 processor that had terrible integer multiplication speed. This fact is why circles and curves were possible on the Macintosh in reasonable drawing time. Source: folklore.org, which has tons of stories from the original Macintosh team.