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From: chuck@bunker.UUCP (Chuck Heaton)
Newsgroups: net.math
Subject: Hoffstuff
Message-ID: <500@bunker.UUCP>
Date: Mon, 20-Aug-84 13:11:59 EDT
Article-I.D.: bunker.500
Posted: Mon Aug 20 13:11:59 1984
Date-Received: Wed, 22-Aug-84 03:38:03 EDT
Lines: 22

Hi.

	Douglas Hoffstadter (sp.?) in his book "Godel, Escher, Bach",
(a wonderful work if you aren't familiar with it) discussed a function
with some rather intriguing properties. The function was defined as
follows:
		h[0] = 0;
		h[k] = k - h[h[k-1]];

	Actually, it is the differences,  g[n] = h[n] - h[n-1] (n>0)
that are most interesting. You can play with the patterns generated
yourself, but what I am concerned with is a definition, recursive
or otherwise, for g[] that does NOT involve h[].
	Any ideas ??? I fooled around with this for awhile and gave
up. Either I have some mental block here, or it realy is a difficult
problem. Any responses to this newsgroup would be greatly
appreciated. Also, any other such 'fun' things would be welcomed with
open arms (& pencil, paper, computer, .....).
	Thanks.

					Chuck Heaton