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 2003-12-05, 13:58 #1 ET_ Banned     "Luigi" Aug 2002 Team Italia 2×29×83 Posts base 3 Here is a thread for which I don't know the answer. I am examining distribution of "0"'s, "1"'s and "2"'s in base 3 powers. Is it homogeneous? Are there infinitely many powers of base-3 integers to justify an equal distribution of numbers in [0..2] in them? Luigi
 2003-12-13, 10:45 #2 tom11784     Aug 2003 Upstate NY, USA 5068 Posts integer powers like 26^2 being 221001 (base3)? if so this is the smallest i can find also, i noticed that depending on the number of each digit desired in the number it determines whether the base 10 number has to be even or odd, and hence whether the a in a^b is odd or even 3 digit representations of powers: 3^2 = 09 ---> 100 4^2 = 16 ---> 121 5^2 = 25 ---> 221 6 digits: 03^5 = 243 ---> 100000 16^2 = 256 ---> 100111 17^2 = 289 ---> 101201 18^2 = 324 ---> 110000 07^3 = 343 ---> 110201 19^2 = 361 ---> 111101 20^2 = 400 ---> 112211 21^2 = 441 ---> 121100 22^2 = 484 ---> 122221 08^3 = 512 ---> 100222 23^2 = 529 ---> 201121 24^2 = 576 ---> 210100 25^2 = 625 ---> 212011 26^2 = 676 ---> 221001 - smallest successful number I don't wanna think about the 9 digit ones at 5:45am

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