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From: tjl@cbnap.UUCP
Newsgroups: net.puzzle
Subject: Another sequence (possible correction) ** SOLUTION **
Message-ID: <178@cbnap.UUCP>
Date: Mon, 27-Feb-84 09:08:10 EST
Article-I.D.: cbnap.178
Posted: Mon Feb 27 09:08:10 1984
Date-Received: Tue, 28-Feb-84 13:31:56 EST
Lines: 64

I haven't seen a solution to the puzzle as origionally posted,
so I'm including the solution to the puzzle in this form...

    1, 110, 111, 100, 101, 11010, 11011, 11000, 11001, ?



the sequence continues...

    11110, 11111, 11100, 11101, 10010, 10011, 10000, ...



SOLUTION 

   .
   .
   .
   .
   .
   .
   .
   .
   .
   .
   .
   .
   .
   .
   .

The sequence is the counting numbers in negabinary (radix -2).
If you've never tried a negative radix before, it is worth exploring
a little.  For example, no unary signs are needed to indicate negative
or positive numbers.  The addition table is...


		      0    1
		    |---------|
		  0 | 0 |  1  |
		    |---------|
		  1 | 1 | 110 |
		    |---------|

Try adding one and negative one.   (Note what happens to carries.)

		 11
		+ 1
		---
		  0

It should be possible to design a computer to use negabinary
arithmetic instead of one or two's complement arithmetic. (There's
a good master's thesis for some EE.)

Using a decimal point for rational values works fine (as would some
sort of floating point standard).

QUESTION:  What happens to logs in negabinary?


By the way, if there is a solution to the problem as origionally
posted (fifth element was 1001 instead of 101), I'd like to see
the solution.