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AntonVrba
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What makes the numbers 142[999]857 special?
1/7 = 0.14285714285714..
1/7 = 0.14285714285714..
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What makes the numbers 142[999]857 special?
- Thread starter AntonVrba
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In summary, the number 142[999]857 is special because when multiplied by 2, 3, 4, 5, and 6, the resulting products are all combinations of the same numbers, regardless of the number of times the nine in the middle is repeated. This unique property makes it one of the only short sequence repeating numbers.
- #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)
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AntonVrba
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142+857=999 is not part of the intended solution
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arildno
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But the rest is?
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Rahmuss
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It only repeats as long as numbers exist?
Individually they are all less than 10?
It is a repeating sequence?
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?
AntonVrba said:
It only repeats as long as numbers exist? Individually they are all less than 10? It is a repeating sequence? 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?
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AntonVrba
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Rahmuss said:
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?
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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.
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
Rahmuss
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AntonVrba said:
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
AntonVrba
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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
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
Rahmuss
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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?
FAQ: What makes the numbers 142[999]857 special?
What is the significance of the number 142[999]857?
The number 142[999]857 is called a repunit prime, which means it is a prime number made up of only repeating digits (in this case, 9s). It is also the smallest repunit prime with 6 repeating digits.
How many digits does 142[999]857 have?
142[999]857 has 10 digits. The digits 1, 4, 2, 8, 5, and 7 each appear once, while the digit 9 appears 6 times.
Is 142[999]857 the largest repunit prime?
No, there are larger repunit primes. However, 142[999]857 is the largest repunit prime with only 6 repeating digits.
Can 142[999]857 be divided by any other number?
No, 142[999]857 can only be divided by 1 and itself, making it a prime number.
Are there any patterns or unique properties related to 142[999]857?
Yes, there are several interesting patterns and properties related to 142[999]857. For example, if you add up all the digits of the number (1+4+2+9+9+9+8+5+7), the result is a multiple of 9. Additionally, if you remove the repeating digits (in this case, the 9s), the remaining number (142857) is also a prime number.