<!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 6.00.2716.2200" name=GENERATOR></HEAD>
<BODY bottomMargin=0 leftMargin=3 topMargin=0 rightMargin=3>
<DIV></DIV>
<DIV> Perhaps A066173 is an
example? </DIV>
<DIV> </DIV>
<DIV> As I calculate it, there is only
one sequence that satisfies the following:</DIV>
<DIV> a(n) = floor(S^n), where S =
sum(k>0, 1/a(k) ), a(1)=1.</DIV>
<DIV> </DIV>
<DIV>Thus the terms are determined uniquely by their reciprocal sum.</DIV>
<DIV> </DIV>
<DIV>The reciprocal sum and the sequence is as follows: </DIV>
<DIV> S = 1.776791425487658...</DIV>
<DIV>and</DIV>
<DIV><STRONG> A066173 =</STRONG>
{1,3,5,9,17,31,55,99,176,313,557,990,1759,3125,5553,...}<BR><BR><STRONG>Example: </STRONG></DIV>
<DIV> 1=[S], 3=[S^2], 5=[S^3],
9=[S^4], 17=[S^5], 31=[S^6], 55=[S^7], ...<BR>where </DIV>
<DIV> S=1/1 + 1/3 + 1/5 + 1/9 + 1/17 +
1/31 + 1/55 + 1/99 + 1/176 +...<BR></DIV>
<DIV>-------------------------------------------------------------------------</DIV>
<DIV>On Thu, 27 Feb 03 19:05:37 -0700 Leroy Quet <<A
href="mailto:qqquet@mindspring.com">qqquet@mindspring.com</A>>
writes:<BR>> I posted this to sci.math. I am asking about any sequence in
general. <BR>> But <BR>> for the purpose of seq.fan, I am asking about
integer sequences.<BR>[...]<BR>> <BR>> I am wondering about any good
examples of infinite sequences where<BR>> every terms depends on every other
term (prior AND following), and<BR>> where there is only one such sequence
which exists given the rule <BR>> that<BR>> generated it.<BR>>
<BR>[...] <BR>> Leroy Quet</DIV></BODY></HTML>