Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Posting-Version: version B 2.10 5/3/83; site metheus.UUCP Path: utzoo!watmath!clyde!burl!mgnetp!ihnp4!mhuxl!ulysses!unc!mcnc!decvax!tektronix!ogcvax!metheus!howard From: howard@metheus.UUCP (Howard A. Landman) Newsgroups: net.math Subject: Re: Iterated sums of digits of divisors Message-ID: <254@metheus.UUCP> Date: Fri, 27-Jul-84 19:45:48 EDT Article-I.D.: metheus.254 Posted: Fri Jul 27 19:45:48 1984 Date-Received: Mon, 30-Jul-84 00:01:31 EDT References: <2976@ecsvax.UUCP> Organization: Metheus, Portland Oregon Lines: 18 Here is an outline of a proof which I am too lazy right now to complete. (1) Prove that for some N, for all M > N, K(M) < M. This establishes that the sequences for all sufficiently large numbers will eventually enter (and STAY in) the set of numbers < N. Thus we only need to consider sequences which start with < N. (2) Any sequence which remains in a finite set must eventually repeat an element. Because of the way this series is calculated, such a repeat means that the series will then repeat a sequence or a single number forever. (3) Prove by exhaustive examination of the cases that there are no such cycles other than 15. (If the statement is false, of course, it is here that you will discover the counterexample.) Howard A. Landman ogcvax!metheus!howard