Oscar Wilde’s character Algernon said in *The Importance of Being Earnest*, “One must be serious about something, if one is to have any amusement in life.” Of course in Wilde’s typical ironic fashion, Algernon was only referring to his own dedication to frivolous diversions. In that spirit, allow me a few moments to tell a story about one of the odder sums of odd integers I discovered as a kid.

I remember that sometimes when I was bored — most especially during long, bi-weekly car trips with my parents — I would play various games with integers. I have no idea why, but at one point I memorized some huge list of powers of 2 (I can still remember the list from 1 to 65,536). I also computed the squares, cubes, and so forth of most of the smaller integers. As a result, I discovered on my own quite a number of interesting patterns in the integers. I don’t remember most of them, but there is one in particular that has stuck with me through the years.