"Eric Angelini" <keynews.tv@skynet.be> wrote:

Hello SeqFan and Math-Fun, Consider this (hope this is not old-hat):

  3^0  3^1  3^2  3^3  3^4  3^5  3^6  3^7 ... =   1    3    9    27   81  243  729  2187 ...

This seq. is known to be very efficient if you want to weigh integer weights with a two-tray balance, leaving no "holes" behind; use weights of 1,3,9,27... units to measure all "natural" quantities, from 1 to infinity:

I had the idea, yesterday night, to represent all natural numbers in the same way -- all I had to do was to use three symbols :  0 for a power of 3 I don't need  1 for a power of 3 I need  2 as a grahic symbol meaning "minus all the    rest"

This is an old idea, but there is a conceptually much simpler approach to the third digit: it is the digit -1, representing putting just this weight in the other pan. The result is called "balanced ternary" - I first encountered it in Knuth's The Art of Computer Programming (I forget which volume). If you use 2 to represent the -1 digit, you will get: 0, 1, 12, 10, 11, 122, 120, 121, 102, 100, 101, ... This sequence is also not in the OEIS. -- Franklin T. Adams-Watters 16 W. Michigan Ave. Palatine, IL 60067 847-776-7645 __________________________________________________________________ Switch to Netscape Internet Service. As low as $9.95 a month -- Sign up today at http://isp.netscape.com/register Netscape. Just the Net You Need. New! Netscape Toolbar for Internet Explorer Search from anywhere on the Web and block those annoying pop-ups. Download now at http://channels.netscape.com/ns/search/install.jsp