Difference between revisions of "142857"

Revision as of 01:52, January 10, 2009

so what?

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-The number '''142857''' has the curious property that, if it is multiplied by any number from 1 to 6, the result is a number with the same digits in the same order (a [[cyclic permutation]]).
+so what?
-For example:
-:142857 &times; 1 = 142857
-:142857 &times; 2 = 285714
-:142857 &times; 3 = 428571
-:142857 &times; 4 = 571428
-:142857 &times; 5 = 714285
-:142857 &times; 6 = 857142
-This property is closely related to the facts that
-:1/7 = 142857/999999
-and that 1/7 expressed as a [[decimal]] is
-:0.142857142857142857142857142857...
-Investigating the number 142857 can lead a student into an understanding of repeating decimals and [[rational numbers]].
-== Similar Numbers ==
-is the only multi-digit decimal number with this property.  However, if leading zeros are allowed on a number, some other examples are:
-:0588235294117647 (16 digits)
-:052631578947368421 (18 digits)
-:0434782608695652173913 (22 digits)
-:0344827586206896551724137931 (28 digits)
-:0212765957446808510638297872340425531914893617 (46 digits)
-In octal (base-8 notation), the numbers 25 and 1463 have this property.  There are no examples in hexadecimal (base-16).
-[[Category:Mathematics]]