What is 142857 and how does this number work?

@DrWatson If it were my Q, I'd award you BEST ANSWER!!

When I'm teaching kids about long division and repeating decimals, I always use 1/9 & its multiples, 1/11 and its multiples, and what you just pointed out about the sevenths.

Then, for extra fun, I ask them to add
1/3=0.33333333333333333333 repeating +
2/3=0.66666666666666666666 repeating =
------------------------------------------------------------------
3/3=.999999999999999999999 repeating
Whoa!!!

@ElwoodBlues Thank you.

The same thing happens when you multiply the decimal from this post by 7, of course .

For those who don't know what a cyclic permutation is:

Let N = 142857.
Then

2N = 285714
3N = 428571
4N = 571428
5N = 714285
6N = 857142

If you start with any of the six digits of 142857 and read from left to right, wrapping around to the first digit after you get to the 7 at the end, you get one of these 6 multiples.

There are plenty of other cyclic numbers, but this is the most famous one.

@DrWatson And when you multiply 142857 by 7 you'll get 999,999.

@ElwoodBlues Looks like most numbers lead to 9.