A sequence unique including differences

Fri May 30 05:17:23 CEST 2008

This is a multipart message in MIME format.

------=_NextPart_000_0001_01C8C24C.C9B14480
Content-Type: text/plain;
	charset="us-ascii"
Content-Transfer-Encoding: 7bit

I believe that:

a(n) = 1 + SUM(k < n; k+f(k+f(k))) where f(n) = MAX {k: a(k) < n}

------=_NextPart_000_0001_01C8C24C.C9B14480
Content-Type: text/html;
	charset="us-ascii"
Content-Transfer-Encoding: quoted-printable

<html xmlns:v=3D"urn:schemas-microsoft-com:vml" xmlns:o=3D"urn:schemas-micr=
osoft-com:office:office" xmlns:w=3D"urn:schemas-microsoft-com:office:word" =
xmlns:m=3D"http://schemas.microsoft.com/office/2004/12/omml" xmlns=3D"http:=
//www.w3.org/TR/REC-html40">

<head>
<meta http-equiv=3DContent-Type content=3D"text/html; charset=3Dus-ascii">
<meta name=3DGenerator content=3D"Microsoft Word 12 (filtered medium)">
<style>
<!--
 /* Font Definitions */
 @font-face
	{font-family:Calibri;
	panose-1:2 15 5 2 2 2 4 3 2 4;}
 /* Style Definitions */
 p.MsoNormal, li.MsoNormal, div.MsoNormal
	{margin:0in;
	margin-bottom:.0001pt;
	font-size:11.0pt;
	font-family:"Calibri","sans-serif";}
a:link, span.MsoHyperlink
	{mso-style-priority:99;
	color:blue;
	text-decoration:underline;}
a:visited, span.MsoHyperlinkFollowed
	{mso-style-priority:99;
	color:purple;
	text-decoration:underline;}
span.EmailStyle17
	{mso-style-type:personal-compose;
	font-family:"Calibri","sans-serif";
	color:windowtext;}
.MsoChpDefault
	{mso-style-type:export-only;}
@page Section1
	{size:8.5in 11.0in;
	margin:1.0in 1.0in 1.0in 1.0in;}
div.Section1
	{page:Section1;}
-->
</style>
<!--[if gte mso 9]><xml>
 <o:shapedefaults v:ext=3D"edit" spidmax=3D"1026" />
</xml><![endif]--><!--[if gte mso 9]><xml>
 <o:shapelayout v:ext=3D"edit">
  <o:idmap v:ext=3D"edit" data=3D"1" />
 </o:shapelayout></xml><![endif]-->
</head>

<body lang=3DEN-US link=3Dblue vlink=3Dpurple>

<div class=3DSection1>

<p class=3DMsoNormal>I believe that:<o:p></o:p></p>

<p class=3DMsoNormal><o:p> </o:p></p>

<p class=3DMsoNormal>a(n) =3D 1 + SUM(k < n; k+f(k+f(k))) where f(n) =3D=
 MAX {k:
a(k) < n}<o:p></o:p></p>

</div>

</body>

</html>

------=_NextPart_000_0001_01C8C24C.C9B14480--