<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
<HTML><HEAD>
<META http-equiv=Content-Type content="text/html; charset=us-ascii">
<META content="MSHTML 6.00.2900.2668"></HEAD>
<BODY>
<DIV><FONT face=Arial size=2><SPAN class=385591916-10052006>In this
query, a(n) and b(n) denote increasing complementary sequences, such
as (1,3,5,7,...) and (2,4,6,8...), as well as pairs of Beatty
sequences.</SPAN></FONT></DIV>
<DIV><FONT face=Arial size=2><SPAN class=385591916-10052006></SPAN></FONT> </DIV>
<DIV><FONT face=Arial size=2><SPAN class=385591916-10052006>The question is, how
can we account for all solutions of the equation </SPAN></FONT></DIV>
<DIV><FONT face=Arial size=2><SPAN class=385591916-10052006></SPAN></FONT><FONT face=Arial size=2><SPAN class=385591916-10052006></SPAN></FONT> </DIV>
<DIV><FONT face=Arial size=2><SPAN class=385591916-10052006>a(b(n)) - b(a(n)) =
1 ?</SPAN></FONT></DIV>
<DIV><FONT face=Arial size=2><SPAN class=385591916-10052006></SPAN></FONT> </DIV>
<DIV><FONT face=Arial size=2><SPAN class=385591916-10052006>Among the solutions
are a = (1,3,5,7,....) and the lower Wythoff sequence, a(n)
= </SPAN></FONT><FONT face=Arial size=2><SPAN class=385591916-10052006>Floor[tau*n)], where tau is the golden
mean.</SPAN></FONT></DIV>
<DIV><FONT face=Arial size=2><SPAN class=385591916-10052006></SPAN></FONT> </DIV>
<DIV><FONT face=Arial size=2><SPAN class=385591916-10052006>Anyone want to
look into this?</SPAN></FONT></DIV>
<DIV><FONT face=Arial size=2><SPAN class=385591916-10052006></SPAN></FONT> </DIV>
<DIV><FONT face=Arial size=2><SPAN class=385591916-10052006>Thanks.</SPAN></FONT></DIV>
<DIV><FONT face=Arial size=2><SPAN class=385591916-10052006></SPAN></FONT> </DIV>
<DIV><FONT face=Arial size=2><SPAN class=385591916-10052006>Clark
Kimberling</SPAN></FONT></DIV>
<DIV><FONT face=Arial size=2><SPAN class=385591916-10052006></SPAN></FONT> </DIV>
<DIV><FONT face=Arial size=2><SPAN class=385591916-10052006></SPAN></FONT> </DIV></BODY></HTML>