24 Sep 2003 major»(Master)

I have found numerous references to some number theory that seems to draw a parallel to my whole computing sum's scenerio that has been driving me crazy as of recent.

The key term is digital root. It seems that my reducing the values of a number to a single digit by adding together each of the digits in the number is computing the digital root. Okay, no biggi there. There also seems to be a semi-weak relation to sigma codes, though I havn't quite decided yet if what I have run across is infact some property of sigma codes or not.

Originally I had used a double itterative loop to compute the digital root, but I have run across a much faster way of computing it for base10 (the 9 can be replaced with baseN - 1):

dr = 1 + (((n ** x) - 1) % 9)

And I have run across a curious conjecture in my recent insanity into this whole thing:

dr(n ** x) = dr(n ** dr(x))

It also seems that: if dr(n) == dr(i) then dr(n ** x) = dr(i ** x)

I am still trying to piece together a proof for this with a friend at work. As soon as we come up with one (more likely he will do all the work here, I am horrible at proofs), we have decided to see about finding a proof that describes the reproducable patterns that occure. And then it is off to explain why it is that predictable powers in the pattern intersect at a digital root of 1 at the same time, and a seperate predictable set of powers never reduce 1, and why it is that these powers are always a fixed distance apart.

New HTML Parser: The long-awaited libxml2 based HTML parser code is live. It needs further work but already handles most markup better than the original parser.

Keep up with the latest Advogato features by reading the Advogato status blog.

If you're a C programmer with some spare time, take a look at the mod_virgule project page and help us with one of the tasks on the ToDo list!