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Lewis Carroll's weird number: 142857
By Charles Wray (M354) on Saturday, February 26, 2000 - 04:44 am:

A number of years ago I read a book of Lewis C.'s miscellaneous writings. He described a very unusual number: 142857 which results from dividing 999999 by 7.

If the number is multiplied consecutively by 2,3,4,5,6, it rotates. e.g., N x 2=285714, N x 3= 428571 and so forth. I wrote a little FORTRAN program that multiplied by every number up to 100 and I continued to see the number there in various combinations, some of which contained fragments of the numbers. Has anyone ever explained this phenomenon ?

By Neil Morrison (P1462) on Saturday, February 26, 2000 - 09:58 pm:

if you take the decimal value of 1/7, you'll find that it is 0.142857 142857 etc (repeating)
2/7 is 0.285714..
3/7 is 0.428571..
4/7 is 0.571428..
5/7 is 0.714285..
6/7 is 0.857142..

There's a fun way of finding the recurring decimal part of a fraction which I will write from memory (ie: its bound to be wrong) [Seems okay to me - The Editor]:

If the fraction is x/N

(x/N)[10N-1 -1] = reccuring part

I think there may be a simpler rearrangement

2/11 gives 18181818 instead of just 18

By The Editor:

It should perhaps be pointed out that the connection between these two facts is that
1000000/7 = 142857.142857142857142857... = 1428571/7
and 999999/7 = 142857.