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Old 2007-06-15, 21:25   #1
davar55
 
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Default All 10 Digits

Find the smallest positive integral value of n
such that the standard decimal representation
for both 2n and 3n
each contains all ten decimal digits.

(What about 4n, 5n, etc. as well?)
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Old 2007-06-16, 00:17   #2
grandpascorpion
 
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for 2 and 3, the answer is 70
2^70 is only the 2nd power of 2 to have all 10 digits

for powers of 4 and 5, the answer is 34


Funny tangent :

2^64 is the lowest power where if you represent the number in bases:3,5,7,9 or 11 (2 is trivial), all the possible digits for base b can be found in the base b representation of number.
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Old 2007-06-17, 06:07   #3
m_f_h
 
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Quote:
Funny tangent :
2^64 is the lowest power where if you represent the number in bases:3,5,7,9 or 11 (2 is trivial), all the possible digits for base b can be found in the base b representation of number.
Nice... but when I wanted to test your statement using the otherwise too cool google calculator, I had to notice that they did not yet implement a "... in base b" (e.g. b=11) feature. (only "in octal", "in hexadecimal" etc works)....
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Old 2007-06-17, 14:35   #4
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Interesting sequence:
http://www.research.att.com/~njas/sequences/A049363

The nth term is the minimum number such that when represented in bases b=2 to n+1, all possible digits for base b are present.

The term they use there is digitally balanced.
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Old 2007-06-17, 15:57   #5
fetofs
 
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I don't quite think so. a(5) is 694, but 694 in base 4 doesn't contain the digit 0. It's simply the first pandigital number in base n. If those two sequences were coincidental, it would be something nice, but I think they aren't.

Last fiddled with by fetofs on 2007-06-17 at 15:59
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Old 2007-06-18, 15:06   #6
grandpascorpion
 
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Ugh, I see my problem. It stems from misreading my output:

This is the sequence that matches my earlier description:

"Smallest integer containing all digits in all bases from 2 to n"
http://www.research.att.com/~njas/se...lish&go=Search

Last fiddled with by grandpascorpion on 2007-06-18 at 15:23
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