If you take any number you can think of, any integer whatsoever, count the number of letters it takes to write it out fully (with or without any 'and's you may need), then take THAT number and repeat the procedure infinitely, what number (or numbers) does this strange series converge to? Is there a unique solution?

Let's face it, this won't be a challenge. But here's an extra thing or two for you. Do you know if this series converges in every language? If the series converges, what number does it converge to? Do they have a unique solution? Can you tell of any language(s) in which does this series not converge?

Note: What if you converted this series into cardinal numbers instead (34 = thirty fourth [12 letters] then 12 = etc.)? How many possible convergence values are there in English or any other language you know?

if you go to this pdf file it has the first dozen ordinal numbers in 8 different languages.

Now german seems to be similar to english in that it has a single cnovergence point of 4.

French is interesting in that it does not have a point convergence but a cyclic.  In French 3 becomes 4 which becomes 6 which becomes 3 again.  All other numbers appear to end up entering this cycle eventually.

Latin is even more interesting in that it has two seperate cycles of convergence namely  4->8->4 and 5->7->5

Posted by Daniel on 2006-09-10 10:33:34