Hi,

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

I definitely came across this idea in the past, sorry... I cannot remember right now, where.

Is the introduction of a third symbol "economi- cally" efficient? (I think we will use less symbols to represent all first 1000 natural integers with this "ternary notation" than with the usual binary system -- the price might be to high, though)...

Speaking in terms of calculations and storage in computers, the binary system has strong technological advantages. It is much easier and more reliable to represent two states than three. E.g. you need only do decide whether there is a certain amount of charge in a capacitor or not. Thus you simply need less chip size (and less power). And I think also the elemental algebraic operations are much simpler (again smaller chip size) in a binary system.

Speaking of "notation efficiency" (how to re- present in the less "symbol-consuming" way all the natural numbers) -- is there a definitive answer?

As far as I remember the optimal base would be exp(1)=2.71... . Therefore 3 may be more efficient than two. But two should be the 2nd best choice regarding efficiency. Best regards Christoph