Actually, I did one of these jumping from one megacorp to another. It took up my entire weekend, but I landed the interview. I then had to take 2 days off to fly out for the interview. Luckily, I got the job.
I can see the pattern: count successive powers of 2, dropping the digit that would occurred. So the next part of the sequence is 123456789012345678901234567891... etc.
But I have no idea how much of the sequence they want me to type in. Very frustrating!
I think I might used this to practice touch typing. It looks addicting :)
I tried to bookmark it by hitting command-D (in Safari on a Mac), but since you capture all keystrokes, I couldn't bookmark it. Perhaps you'd see a bump in your numbers if you allowed command-D through?