Divine Lunacy

So, Dave came to me with a math problem….A really really hard one, yet really really simple. The numbers seem to have nothing in common, because they don’t.

1
11
21
1211
111221
312211
???

what comes next in the sequence?
Well, the numbers do actually seem to have something in common, not exactly sure if it can be expressed mathematically though. I tried dividing them, with eachother and other common numbers, and subtracting them…Odd similarities apeared but nothing large enough to draw a conclusion from. It was then that I was pretty sure there was something going on at a digital level….But what? I looked at every different way to move the digits around, and found no common pattern. It was beginning to get disgusting, when all of a sudden, I looked at the first 3 for the millionth time….ahha! “one one” “two ones”…there was definitely a pattern there. Notice how each nubmer after the first has an even number of digits? Every two digits forms a summary of the number above it in the sequence
31—22—11=”three ones”, “two twos”, “one one”…it spells out the one before it in the sequence. So the next number is “one three”,”one one”,”two twos”,”two ones”

OH YEah!~

This entry was posted on Monday, September 20th, 2004 at 2130:54 and is filed under General. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.