19 Sep 2003 major   » (Master)

Okay, so I managed to get dragged out of my cave I dwell in and into the world again, tossed at the doorsteps to this site.

The trust metric is a curious concept. I recognize the reasons for using it, and at the same time I worry. In the end I guess it all comes down to how open the users are to certifying people who have different points of view, potentially conflicting ones. Only time will tell I guess, though it might be interesting to graph out.

On that note, I ran across a curious pattern the other night, summing up the values of each of the values of base2 powers. i.e.

1 = 1, 2 = 2, 4 = 4, 8 = 8, 16 = 1 + 6 = 7, 32 = 3 + 2 = 5, 64 = 6 + 4 = 10 = 1 + 0 = 1

So on and so forth. There is a pattern that shows up if you carry it out far enough.

1, 2, 4, 8, 7, 5, 1, 2, 4, 8, 7, 5 ...

The pattern continues on indeffinately it seems, or at least it did when computing to 2^1000. A similar pattern arives for base4 when representing the sums in base10, 1 4 7 1 4 7, and base5 is the inverse of base2, 5 7 8 4 2 1. Base7 seems to be the inverse of base 4, 7 4 1 7 4 1. Base3, 6, and 9 all end up sum'ing to 9 over and over again (with the exception of the first couple of powers), base 8 to 1 8 1 8 1 8.

If you go higher up the bases, like base31, you find the same pattern as base4 (3 + 1 = 4, odd coincidence), and base23 has the same pattern as base5 (2+3?). In the end, everything above base9 generated a pattern that matched one of the base1-9 patterns.

The only bases to not generate an infinite list of 9's where base 1, 2, 4, 8, 7 and 5 patterns, which are the same numbers for base2 and base5. I have been meaning to go see if such a mundane thing as reducing the sums in such a way was ever noticed before and documented, but I keep forgetting to. Maybe this entry will serve as a reminder. It all graphs out very curiously, though for the most part it seems to be no more usefull then helping one go to sleep at night.

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