A web site devoted to the number 142857.
1/7 = 0.142857142857142857142857142857142857...
and, for example, 142857 * 2 = 285714 -- the same digits, but in a different order.
There are some facts I hadn't seen, too, like 8572 - 1422 = 714285, and the pair 1428572 = 20408122449, 20408+12249 = 142857. The first one has a nice "approximate" explanation, namely that (6/7)2 - (1/7)2 = 5/7 (multiply both sides by 106), but I don't even see why the second one has any chance of being true.
17 September 2007
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3 comments:
Well I think you just gave them a lot of traffic, I went to look and their bandwidth was exceeded.
There was once a site for pi and e; I haven't look for them for a while.
michael,
I don't have that sort of effect. I learned about the site from reddit.com.
Look at the tails. divide to find:
999999 = 20408 * 49 + 7
and thus:
(10^6 - 1)/49 = 20408 + 7/49 = 20408 + 1/7
but we know:
1/7 = 142857/(10^6 - 1)
so we can calculate
(10^6 - 1)/49 =
(10^6 - 1) * 142857^2/(10^6 - 1)^2 =
20408122449/(10^6-1)
And now the geometric series says this is:
20408122449 * \sum_{i=1}^\infty 10^{-6i} =
20408.122449 +
0.020408122449 +
...
See it now?
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