The Number Four

I recently saw a video posted to YouTube that explained an interesting property about the number four. Demonstrations are always the best way to start an explanation, so here we go:

Pick any positive integer. Write that number in words. For example, if I chose 10, then I would write out ‘ten.’ Count the number of letters in the result. In this case, we get 3. Now rinse and repeat the process. 3 is spelled three and there are 5 letters. 5 is spelled five, which has four letters.

And so we arrive at the number four and stay there, since four has 4 letters.

After I watched the video, I tried a few examples on my own. I’d encourage you to do the same. But after doing this a couple of times, I wondered if there might be a better way. Would it be possible to find some sort of web API that could take any number and return that number in words? If so, I could write a computer program that could check any number to see if the pattern held. I could also easily start to investigate the resulting sequence and look for other patterns.