base 3

ET_ · 2003-12-05, 13:58

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

tom11784 · 2003-12-13, 10:45

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

2003-12-05, 13:58	#1
ET_ Banned "Luigi" Aug 2002 Team Italia 3²×5×107 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

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2003-12-13, 10:45	#2
tom11784 Aug 2003 Upstate NY, USA 2·163 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