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What is 142857 and how does this number work?

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DrWatson · 70-79, M
It is the repeating block of digits in the repeating decimal expansion of the fraction 1/7.

It has the interesting property that if you multiply it by 2, 3, 4, 5, or 6 ( to obtain the decimals for 2/7, 3/7, etc.), it is transformed into a cyclic permutation of itself.
DrWatson · 70-79, M
@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.
Tennessee · 46-50, F
@DrWatson And when you multiply 142857 by 7 you'll get 999,999.
Tennessee · 46-50, F
@ElwoodBlues Looks like most numbers lead to 9.
Peaceandnamaste · 26-30, F
A cyclical number that corresponds with the patterns and cycles of the cosmos and nature.


2 times 7 is 14, We have 14 days that equals 2 weeks

28 days equals 4 weeks lunar and reproductive cycles and February has 28 days and 29 days for leap years.

2 times 7 equals 14

2 times 7 plus 14 equals 28.

2 times 7 plus 43 equals 57
DrWatson · 70-79, M
@Peaceandnamaste

2 times 7 plus 7 is 21, not 28.
Peaceandnamaste · 26-30, F
@DrWatson oops sorry I meant

2 times 7 plus 14=28 about to edit it.
Barebum61 · 61-69, M
1x1=1
2÷8=4
5-7=2
4×2=8
4+1=5
5+2=7
It's all in the maths

 
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