Ever heard of Dudeney numbers? Neither had I, until yesterday, when I discovered them completely by accident while reading (Wikipedia, what else?) about narcissistic numbers. A Dudeney number (named after famous English mathematician and puzzle author Henry Dudeney) is a number that is the cube of the sum of its digits. For example,

There are only six Dudeney numbers. Neat numbers, but I was a little disappointed by that. What to do next?

Generalize, of course! Generalized Dudeney numbers (discussed here, but the link appears to be dead, so I used Google’s cached version) are numbers that are some power of the sum of their digits:

The largest number on the above site is , which has 147253 digits. The site links to Wolfram Alpha to confirm this. Here’s where it gets weird:

How many digits is that? About ? About *a million*? What kind of rounding is that? It gets worse. Try a number with just 100,002 digits (despite what Alpha says). I think Alpha is a great tool, and I’ve had (far too much) fun playing with it, but I’m a tad disappointed (that’s twice in one post). So, hey, get on that, Wolfram.