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 2007-06-15, 21:25 #1 davar55     May 2004 New York City 5·7·112 Posts 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?)
 2007-06-16, 00:17 #2 grandpascorpion     Jan 2005 Transdniestr 503 Posts 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.
2007-06-17, 06:07   #3
m_f_h

Feb 2007

43210 Posts

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)....

 2007-06-17, 14:35 #4 grandpascorpion     Jan 2005 Transdniestr 503 Posts 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.
 2007-06-17, 15:57 #5 fetofs     Aug 2005 Brazil 2·181 Posts 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
 2007-06-18, 15:06 #6 grandpascorpion     Jan 2005 Transdniestr 503 Posts Correction 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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