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What makes the numbers 142[999]857 special?

  1. May 24, 2005 #1
    What makes the numbers 142[999]857 special?

    1/7 = 0.14285714285714..
     
    Last edited: May 24, 2005
  2. jcsd
  3. May 24, 2005 #2

    arildno

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    Well, 142+857=999, and I would assume that 142999857 is divisible with 142,999 and 857 (I haven't checked the divisibility criterion though)
     
  4. May 24, 2005 #3
    142+857=999 is not part of the intended solution
     
  5. May 24, 2005 #4

    arildno

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    But the rest is?
     
  6. May 24, 2005 #5
    Master of the Obvious

    :uhh: It only repeats as long as numbers exist??? :surprised

    :uhh: Individually they are all less than 10??? :surprised

    :uhh: It is a repeating sequence??? :surprised

    :uhh: 1+4-2+8-5+7 = 13 and 1-4+2-8+5-7 = -11 with 13-11 = 2 which is "14"/7 and "28"/7 = 4 which is twice 2 and "57" doesn't matter at all because it already has a "7" in it.

    It is one of the only short sequence repeating numbers???
     
  7. May 24, 2005 #6
    nice try but none of these or others above

    but I like the bit about repeating but what repeats?
     
  8. May 25, 2005 #7

    James R

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    There's nothing special about 142857.

    For example:

    1/17 = 0.0588235294117647 0588235294117647 0588235294117647 ...
    2/17 = 0.1176470588235294 1176470588235294 1176470588235294 ...
    3/17 = 0.1764705882352941 1764705882352941 1764705882352941 ...

    Notice the cyclic nature of the decimal expansion.
     
  9. May 25, 2005 #8
    Well... the "142857" repeats; but that isn't really too special. I'm really either not sure what you're asking, or I'm stumped.
     
  10. May 25, 2005 #9
    OK - her is the answer

    2 x 142[999]857 = 285[999]714
    3 x 142[999]857 = 428[999]571
    upto
    6 x 142[999]857= 857[999]124

    the product 2x, 3x, 4x, 5x, 6x of 142[999]857 is always a combination of the same numbers, irrespective of how many times you repeat the nine in the middle
     
  11. May 25, 2005 #10
    Wow! That is kind of neat. Go into the number theory forum and see if they can give a good reason as to why that is. Or do you know why that is?
     
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