What makes the numbers 142[999]857 special?

  • Thread starter AntonVrba
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  • #1
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What makes the numbers 142[999]857 special?

1/7 = 0.14285714285714..
 
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  • #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)
 
  • #3
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142+857=999 is not part of the intended solution
 
  • #4
arildno
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But the rest is?
 
  • #5
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Master of the Obvious

AntonVrba said:
What makes the numbers 142[999]857 special?

1/7 = 0.14285714285714..
: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???
 
  • #6
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Rahmuss said:
: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???
nice try but none of these or others above

but I like the bit about repeating but what repeats?
 
  • #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.
 
  • #8
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AntonVrba said:
nice try but none of these or others above

but I like the bit about repeating but what repeats?
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.
 
  • #9
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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
 
  • #10
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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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