1. use as many of the first 10,000 digits of pi (here) as you need
and, because I think you'll tend to get a bias towards the early letters of the alphabet (and, hence, more chance of a loop):
2. count along the friends list starting from the first username that starts with the last letter of the previous username (0 = select the first name); start with the last letter of your username
3. if there isn't a username that fits 2, start from the next letter along
4. if you get to the end of the list, start again at the beginning
Hang on a moment - I've misunderstood the rules! I'm counting along the list of friends in the userinfo section (ie the alphabetical list) not in the friends entry view...
I'm sticking with my misinterpretation as it removes a bias towards people who post often.
3 (from y, looping round): alfaguru talking about a trip to Ireland and his odd books site - previous post concerns a book that offers a mathematical proof of the bible
1 (from u): verlaine photos from the Disneyland (?) walk of fame from his American odyssey, plus the list of CDs he took with him.
4 (from e): eldar a meme (skipped), positive review of "His Dark Materials" at the National Theatre.
1 (from r): sigje brain gender meme, some stuff about the AC (took me a while to work out this was the air conditioning)
5 (from e): ginmar death penalty discussion (brief post followed by lengthy discussion in the comments)
9 (from r): rivkat fantastic link to an Azlan Prayer Ministry questionnaire.
2 (from t): taraljc much excitement about galaxy_rangers.
6 (from c): cecily_v some drooling over Simon (from Firefly) and his appearance on CSI: Miami. First really old post (April 29th 2003).
5 (from v, looping round): fox1013 general bitching and the prospect of a room being cleaned.
3 (from 3 - comes before 'a', I suppose): abbylee "10 things" meme (skipped); cool post about craving books and music, plus a list of recent purchases.
5 (from e): elke_tanzer Mind boggling posts catching up with a load of LJ friends plus some fanfic stuff that I don't really follow.
8 (from r): reetchick Some grumbling that I can't follow and an "SV Fic" that I have absolutely no idea about.
9 (from k): ladyvyola Some links and an Oscar coverage grumble.
7 (from a): calligrafiti Some low-carb diet stuff and something about a "Naveen Icon" that I don't understand.
9 (from i): julad General stuff about work and friends and buying an iPod.
3 (from d): dr_speranza Future-dated "books to get" list, link to a piece about collaboration and originality.
2 (from a): rivkat And that's the loop - bit of a fan-fic loop.