CINXE.COM

<!DOCTYPE html> <html class="client-nojs" lang="en" dir="ltr"> <head> <meta charset="UTF-8"/> <title>OeisWiki:Community Portal - OeisWiki</title> <script>document.documentElement.className = document.documentElement.className.replace( /(^|\s)client-nojs(\s|$)/, "$1client-js$2" );</script> <script>(window.RLQ=window.RLQ||[]).push(function(){mw.config.set({"wgCanonicalNamespace":"Project","wgCanonicalSpecialPageName":false,"wgNamespaceNumber":4,"wgPageName":"OeisWiki:Community_Portal","wgTitle":"Community Portal","wgCurRevisionId":1572209,"wgRevisionId":1546380,"wgArticleId":177028,"wgIsArticle":true,"wgIsRedirect":false,"wgAction":"view","wgUserName":null,"wgUserGroups":["*"],"wgCategories":[],"wgBreakFrames":false,"wgPageContentLanguage":"en","wgPageContentModel":"wikitext","wgSeparatorTransformTable":["",""],"wgDigitTransformTable":["",""],"wgDefaultDateFormat":"dmy","wgMonthNames":["","January","February","March","April","May","June","July","August","September","October","November","December"],"wgMonthNamesShort":["","Jan","Feb","Mar","Apr","May","Jun","Jul","Aug","Sep","Oct","Nov","Dec"],"wgRelevantPageName":"OeisWiki:Community_Portal","wgRelevantArticleId":177028,"wgRequestId":"2923fe54f9c27e03c8c01187","wgIsProbablyEditable":false,"wgRelevantPageIsProbablyEditable":false,"wgRestrictionEdit":[],"wgRestrictionMove":[],"wgRedirectedFrom":"OeisWiki:About","wgFlaggedRevsParams":{"tags":{"style":{"levels":2,"quality":2,"pristine":4}}},"wgStableRevisionId":1546380,"wgInternalRedirectTargetUrl":"/wiki/OeisWiki:Community_Portal"});mw.loader.state({"site.styles":"ready","noscript":"ready","user.styles":"ready","user":"ready","user.options":"loading","user.tokens":"loading","ext.flaggedRevs.basic":"ready","mediawiki.legacy.shared":"ready","mediawiki.legacy.commonPrint":"ready","mediawiki.sectionAnchor":"ready","mediawiki.skinning.interface":"ready","mediawiki.skinning.content.externallinks":"ready","skins.monobook.styles":"ready"});mw.loader.implement("user.options@0bhc5ha",function($,jQuery,require,module){mw.user.options.set([]);});mw.loader.implement("user.tokens@0jlvv7z",function ( $, jQuery, require, module ) { mw.user.tokens.set({"editToken":"+\\","patrolToken":"+\\","watchToken":"+\\","csrfToken":"+\\"});/*@nomin*/ });mw.loader.load(["mediawiki.action.view.redirect","site","mediawiki.page.startup","mediawiki.user","mediawiki.hidpi","mediawiki.page.ready","mediawiki.toc","mediawiki.searchSuggest","ext.flaggedRevs.advanced"]);});</script> <link rel="stylesheet" href="/w/load.php?debug=false&lang=en&modules=ext.flaggedRevs.basic%7Cmediawiki.legacy.commonPrint%2Cshared%7Cmediawiki.sectionAnchor%7Cmediawiki.skinning.content.externallinks%7Cmediawiki.skinning.interface%7Cskins.monobook.styles&only=styles&skin=monobook"/> <script async="" src="/w/load.php?debug=false&lang=en&modules=startup&only=scripts&skin=monobook"></script>  <meta name="ResourceLoaderDynamicStyles" content=""/> <meta name="generator" content="MediaWiki 1.30.0"/> <link rel="shortcut icon" href="/favicon.ico"/> <link rel="search" type="application/opensearchdescription+xml" href="/w/opensearch_desc.php" title="OeisWiki (en)"/> <link rel="EditURI" type="application/rsd+xml" href="https://oeis.org/w/api.php?action=rsd"/> <link rel="license" href="/wiki/The_OEIS_End-User_License_Agreement"/> <link rel="alternate" type="application/atom+xml" title="OeisWiki Atom feed" href="/w/index.php?title=Special:RecentChanges&feed=atom"/> <link rel="canonical" href="https://oeis.org/wiki/OeisWiki:Community_Portal"/>  </head> <body class="mediawiki ltr sitedir-ltr mw-hide-empty-elt ns-4 ns-subject page-OeisWiki_Community_Portal rootpage-OeisWiki_Community_Portal skin-monobook action-view"><div id="globalWrapper"> <div id="column-content"> <div id="content" class="mw-body" role="main"> <a id="top"></a> <div id="siteNotice" class="mw-body-content"><div id="localNotice" lang="en" dir="ltr"><div class="mw-parser-output"><p>This site is supported by donations to <a rel="nofollow" class="external text" href="http://oeisf.org/">The OEIS Foundation</a>. </p></div></div></div> <div class="mw-indicators mw-body-content"> </div> <h1 id="firstHeading" class="firstHeading" lang="en">OeisWiki:Community Portal</h1> <div id="bodyContent" class="mw-body-content"> <div id="siteSub">From OeisWiki</div> <div id="contentSub"><span class="mw-redirectedfrom">(Redirected from <a href="/w/index.php?title=OeisWiki:About&redirect=no" class="mw-redirect" title="OeisWiki:About">OeisWiki:About</a>)</span><br /> <div id="mw-fr-revisiontag" class="flaggedrevs_quality flaggedrevs_stable_notsynced plainlinks noprint nomobile"><img class="flaggedrevs-icon" src="/w/extensions/FlaggedRevs/frontend/modules/img/3.png" alt="This is a quality version of this page" title="This is a quality version of this page" />This is the <a href="/wiki/Help:Page_validation" title="Help:Page validation">stable version</a>, <a rel="nofollow" class="external text" href="https://oeis.org/w/index.php?title=Special:Log&type=review&page=OeisWiki:Community_Portal">approved</a> on <i>27 September 2011</i>. <a rel="nofollow" class="external text" href="https://oeis.org/w/index.php?title=OeisWiki:Community_Portal&oldid=1546380&diff=cur">3 pending changes</a> await review.<a id="mw-fr-revisiontoggle" class="fr-toggle-symbol" style="display:none;" title="show/hide details" >(+)</a><div id='mw-fr-revisiondetails'> <span class='fr-marker-60'><strong>Readability</strong>: <span class='fr-text-value'>Approved </span> </span> </div></div> </div> <div id="jump-to-nav" class="mw-jump">Jump to: <a href="#column-one">navigation</a>, <a href="#searchInput">search</a></div>  <div id="mw-content-text" lang="en" dir="ltr" class="mw-content-ltr"><div class="mw-parser-output"><div id="toc" class="toc"><div class="toctitle"><h2>Contents</h2></div> <ul> <li class="toclevel-1 tocsection-1"><a href="#A_few_preliminary_pages_.28most_of_these_need_to_be_updated.21.29"><span class="tocnumber">1</span> <span class="toctext">A few preliminary pages (most of these need to be updated!)</span></a></li> <li class="toclevel-1"><a href="#Sequence_of_the_Day_for_December_1"><span class="tocnumber">2</span> <span class="toctext">Sequence of the Day for December 1</span></a></li> </ul> </div> <p>This page contains notes about the status of the OEIS wiki. It provides a brief description of the wiki setup. It will also be used to announce changes in the structure of the wiki, so it may be useful to add it to your <a href="/wiki/Special:Watchlist" title="Special:Watchlist">watchlist</a> by clicking on the watch tab at the top of the page. </p><p>Users can create and modify discussion pages here. The discussion pages are a reasonable place to make comments about the structure of the wiki. </p><p>Do not use the discussion pages to suggest changes to OEIS sequence entries. </p><p><b>An account is necessary to contribute to the Wiki. <a href="/wiki/Special:RequestAccount" title="Special:RequestAccount">To request an account, click here</a></b>. There was a time when the username was required to be your Real Name. This is no longer required, but is <b>strongly</b> recommended. If this evolving statement causes you to want to change your username, send email to <a href="/wiki/Special:EmailUser/David_Applegate" title="Special:EmailUser/David Applegate">David</a>, and I can make the change. </p> <h2><span class="mw-headline" id="A_few_preliminary_pages_.28most_of_these_need_to_be_updated.21.29">A few preliminary pages (most of these need to be updated!)</span></h2> <ul><li> <a href="/wiki/Motivation" title="Motivation">Motivation for the wiki</a></li> <li> <a href="/wiki/ToDo" title="ToDo">Known things to do</a></li> <li> <a href="/wiki/Issues" title="Issues">Known questions that need to be decided</a></li> <li> <a href="/wiki/Road_map" title="Road map">Road map for wiki migration</a></li> <li> <a href="/wiki/OeisWiki:System_Status" title="OeisWiki:System Status">System Status</a></li> <li> <a href="/wiki/New_Users" title="New Users">Information for new users</a></li> <li> <a href="/wiki/FAQ" title="FAQ">FAQ</a></li></ul> <div style="float:right; clear:both; margin-top: 0.75em;">[<a href="/w/index.php?title=Template_talk:Sequence_of_the_Day_for_December_1&action=edit&redlink=1" class="new" title="Template talk:Sequence of the Day for December 1 (page does not exist)">talk</a>]</div> <h2><span class="mw-headline" id="Sequence_of_the_Day_for_December_1">Sequence of the Day for December 1</span></h2> <a href="http://oeis.org/A188892">A188892</a>: Numbers <span class="math, textstyle" style="display: inline-block; margin: 0 0 -0.75ex 0; padding: 0; white-space: nowrap; position: relative; vertical-align: -0.1ex; font-size: 1.15em; font-family: 'Computer Modern', STIXGeneral, 'Times New Roman';" title="\textstyle { n }"><span style="display: inline-block; margin: 0; padding: 0; position: relative; vertical-align: -0.6ex;"><table style="display: inline-table; position: relative; vertical-align: baseline; margin: 0; padding: 0; border-width: 0; border-spacing: 0; background: transparent;"><tr><td style="margin: 0; padding: 0;"><i>n</i></td></tr></table></span></span> such that there is no triangular <span class="math, textstyle" style="display: inline-block; margin: 0 0 -0.75ex 0; padding: 0; white-space: nowrap; position: relative; vertical-align: -0.1ex; font-size: 1.15em; font-family: 'Computer Modern', STIXGeneral, 'Times New Roman';" title="\textstyle { n }"><span style="display: inline-block; margin: 0; padding: 0; position: relative; vertical-align: -0.6ex;"><table style="display: inline-table; position: relative; vertical-align: baseline; margin: 0; padding: 0; border-width: 0; border-spacing: 0; background: transparent;"><tr><td style="margin: 0; padding: 0;"><i>n</i></td></tr></table></span></span>-gonal number greater than <span class="math" style="white-space: nowrap; font-size: 1.15em; font-family: 'Computer Modern', STIXGeneral, 'Times New Roman';">1</span>. <dl><dd> <div style="margin: 0.5ex 0 0 0; font-size: 1.75em; text-align: baseline; background-color: transparent;"><div class="integer sequence" style="display: inline-block; font-size: 1.15em; font-family: 'Computer Modern', STIXGeneral, 'Times New Roman';">{ 11, 18, 38, 102, 198, 326, 486, ... }</div></div></dd></dl> The <a href="/wiki/Triangular_numbers" title="Triangular numbers">triangular numbers</a> are essentially the building blocks of the other <a href="/wiki/Figurate_numbers" title="Figurate numbers">figurate numbers</a>. Therefore it is rather surprising that there can be sequences of <span class="math, textstyle" style="display: inline-block; margin: 0 0 -0.75ex 0; padding: 0; white-space: nowrap; position: relative; vertical-align: -0.1ex; font-size: 1.15em; font-family: 'Computer Modern', STIXGeneral, 'Times New Roman';" title="\textstyle { n }"><span style="display: inline-block; margin: 0; padding: 0; position: relative; vertical-align: -0.6ex;"><table style="display: inline-table; position: relative; vertical-align: baseline; margin: 0; padding: 0; border-width: 0; border-spacing: 0; background: transparent;"><tr><td style="margin: 0; padding: 0;"><i>n</i></td></tr></table></span></span>-gonal numbers that don鈥檛 overlap with the sequence of triangular numbers at all (other than <span class="math" style="white-space: nowrap; font-size: 1.15em; font-family: 'Computer Modern', STIXGeneral, 'Times New Roman';">0</span> and <span class="math" style="white-space: nowrap; font-size: 1.15em; font-family: 'Computer Modern', STIXGeneral, 'Times New Roman';">1</span>). <a href="/wiki/User:T._D._Noe" title="User:T. D. Noe">T. D. Noe</a> has demonstrated that the equation <span class="math, textstyle" style="display: inline-block; margin: 0 0 -0.75ex 0; padding: 0; white-space: nowrap; position: relative; vertical-align: -0.1ex; font-size: 1.15em; font-family: 'Computer Modern', STIXGeneral, 'Times New Roman';" title="\textstyle { x^2 + x = (n - 2) \, y^2 - (n - 4) \, y }"><span style="display: inline-block; margin: 0; padding: 0; position: relative; vertical-align: -0.6ex;"><table style="display: inline-table; position: relative; vertical-align: baseline; margin: 0; padding: 0; border-width: 0; border-spacing: 0; background: transparent;"><tr><td style="margin: 0; padding: 0;"><i>x</i><span style="position: relative; vertical-align: 1.25ex; line-height: 0.75ex; font-size: 0.75em;"><span style="position: relative; vertical-align: middle;"> 2</span></span> + <i>x</i> = (<i>n</i>  −  2) <i>y</i><span style="position: relative; vertical-align: 1.25ex; line-height: 0.75ex; font-size: 0.75em;"><span style="position: relative; vertical-align: middle;"> 2</span></span>  −  (<i>n</i>  −  4) <i>y</i></td></tr></table></span></span> has no integer solutions <span class="math, textstyle" style="display: inline-block; margin: 0 0 -0.75ex 0; padding: 0; white-space: nowrap; position: relative; vertical-align: -0.1ex; font-size: 1.15em; font-family: 'Computer Modern', STIXGeneral, 'Times New Roman';" title="\textstyle { x \ge y > 1 }"><span style="display: inline-block; margin: 0; padding: 0; position: relative; vertical-align: -0.6ex;"><table style="display: inline-table; position: relative; vertical-align: baseline; margin: 0; padding: 0; border-width: 0; border-spacing: 0; background: transparent;"><tr><td style="margin: 0; padding: 0;"><i>x</i>   ≥   <i>y</i> > 1</td></tr></table></span></span>, as conversion to a <a href="/wiki/Generalized_Pell_equation" class="mw-redirect" title="Generalized Pell equation">generalized Pell equation</a> shows that if <span class="math, textstyle" style="display: inline-block; margin: 0 0 -0.75ex 0; padding: 0; white-space: nowrap; position: relative; vertical-align: -0.1ex; font-size: 1.15em; font-family: 'Computer Modern', STIXGeneral, 'Times New Roman';" title="\textstyle { n = k^2 + 2 }"><span style="display: inline-block; margin: 0; padding: 0; position: relative; vertical-align: -0.6ex;"><table style="display: inline-table; position: relative; vertical-align: baseline; margin: 0; padding: 0; border-width: 0; border-spacing: 0; background: transparent;"><tr><td style="margin: 0; padding: 0;"><i>n</i> = <i>k</i><span style="position: relative; vertical-align: 1.25ex; line-height: 0.75ex; font-size: 0.75em;"><span style="position: relative; vertical-align: middle;">  2</span></span> + 2</td></tr></table></span></span>, then the first equation has only a finite number of solutions. From there one can pinpoint those values of <span class="math, textstyle" style="display: inline-block; margin: 0 0 -0.75ex 0; padding: 0; white-space: nowrap; position: relative; vertical-align: -0.1ex; font-size: 1.15em; font-family: 'Computer Modern', STIXGeneral, 'Times New Roman';" title="\textstyle { n }"><span style="display: inline-block; margin: 0; padding: 0; position: relative; vertical-align: -0.6ex;"><table style="display: inline-table; position: relative; vertical-align: baseline; margin: 0; padding: 0; border-width: 0; border-spacing: 0; background: transparent;"><tr><td style="margin: 0; padding: 0;"><i>n</i></td></tr></table></span></span> that produce no integer solutions greater than <span class="math" style="white-space: nowrap; font-size: 1.15em; font-family: 'Computer Modern', STIXGeneral, 'Times New Roman';">1</span>.   </div>  </div><div class="printfooter"> Retrieved from "<a dir="ltr" href="https://oeis.org/w/index.php?title=OeisWiki:Community_Portal&oldid=1546380">https://oeis.org/w/index.php?title=OeisWiki:Community_Portal&oldid=1546380</a>"</div> <div id="catlinks" class="catlinks catlinks-allhidden" data-mw="interface"></div>  <div class="visualClear"></div> </div> </div> </div> <div id="column-one"> <h2>Navigation menu</h2> <div id="p-cactions" class="portlet" role="navigation"> <h3>Views</h3> <div class="pBody"> <ul> <li id="ca-nstab-project" class="selected"><a href="/wiki/OeisWiki:Community_Portal" title="View the project page [a]" accesskey="a">Project page</a></li> <li id="ca-talk"><a href="/wiki/OeisWiki_talk:Community_Portal" rel="discussion" title="Discussion about the content page [t]" accesskey="t">Discussion</a></li> <li id="ca-view" class="selected"><a href="/w/index.php?title=OeisWiki:Community_Portal&stable=1">View</a></li> <li id="ca-current" class="collapsible"><a href="/w/index.php?title=OeisWiki:Community_Portal&stable=0&redirect=no" title="View this page with the pending changes [v]" accesskey="v">Pending changes</a></li> <li id="ca-viewsource"><a href="https://oeis.org/w/index.php?title=OeisWiki:Community_Portal&action=edit" title="This page is protected.
You can view its source [e]" accesskey="e">View source</a></li> <li id="ca-history"><a href="/w/index.php?title=OeisWiki:Community_Portal&action=history" title="Past revisions of this page [h]" accesskey="h">History</a></li> </ul> </div> </div> <div class="portlet" id="p-personal" role="navigation"> <h3>Personal tools</h3> <div class="pBody"> <ul> <li id="pt-login"><a href="/w/index.php?title=Special:UserLogin&returnto=OeisWiki%3ACommunity+Portal" title="You are encouraged to log in; however, it is not mandatory [o]" accesskey="o">Log in</a></li> <li id="pt-createaccount"><a href="/wiki/Special:RequestAccount" title="You are encouraged to create an account and log in; however, it is not mandatory">Request account</a></li> </ul> </div> </div> <div class="portlet" id="p-logo" role="banner"> <a href="/wiki/Main_Page" class="mw-wiki-logo" title="Visit the main page"></a> </div> <div class="generated-sidebar portlet" id="p-navigation" role="navigation"> <h3>Navigation</h3> <div class="pBody"> <ul> <li id="n-OEIS"><a href="http://oeis.org/">OEIS</a></li> <li id="n-mainpage-description"><a href="/wiki/Main_Page" title="Visit the main page [z]" accesskey="z">Wiki Main Page</a></li> <li id="n-portal"><a href="/wiki/OeisWiki:Community_portal" title="About the project, what you can do, where to find things">Community portal</a></li> <li id="n-status"><a href="/wiki/OeisWiki:System_Status">System Status</a></li> <li id="n-recentchanges"><a href="/wiki/Special:RecentChanges" title="A list of recent changes in the wiki [r]" accesskey="r">Recent changes</a></li> <li id="n-randompage"><a href="/wiki/Special:Random" title="Load a random page [x]" accesskey="x">Random page</a></li> <li id="n-help"><a href="https://www.mediawiki.org/wiki/Special:MyLanguage/Help:Contents" title="The place to find out">Help</a></li> </ul> </div> </div> <div id="p-search" class="portlet" role="search"> <h3><label for="searchInput">Search</label></h3> <div id="searchBody" class="pBody"> <form action="/w/index.php" id="searchform"> <input type="hidden" name="title" value="Special:Search"/> <input type="search" name="search" placeholder="Search OeisWiki" title="Search OeisWiki [f]" accesskey="f" id="searchInput"/> <input type="submit" name="go" value="Go" title="Go to a page with this exact name if it exists" id="searchGoButton" class="searchButton"/> <div><a href="/wiki/Special:Search" rel="search">Advanced search</a></div> </form> </div> </div> <div class="portlet" id="p-tb" role="navigation"> <h3>Tools</h3> <div class="pBody"> <ul> <li id="t-whatlinkshere"><a href="/wiki/Special:WhatLinksHere/OeisWiki:Community_Portal" title="A list of all wiki pages that link here [j]" accesskey="j">What links here</a></li> <li id="t-recentchangeslinked"><a href="/wiki/Special:RecentChangesLinked/OeisWiki:Community_Portal" rel="nofollow" title="Recent changes in pages linked from this page [k]" accesskey="k">Related changes</a></li> <li id="t-specialpages"><a href="/wiki/Special:SpecialPages" title="A list of all special pages [q]" accesskey="q">Special pages</a></li> <li id="t-print"><a href="/w/index.php?title=OeisWiki:Community_Portal&printable=yes" rel="alternate" title="Printable version of this page [p]" accesskey="p">Printable version</a></li> <li id="t-permalink"><a href="/w/index.php?title=OeisWiki:Community_Portal&oldid=1546380" title="Permanent link to this revision of the page">Permanent link</a></li> <li id="t-info"><a href="/w/index.php?title=OeisWiki:Community_Portal&action=info" title="More information about this page">Page information</a></li> </ul> </div> </div> </div> <div class="visualClear"></div> <div id="footer" role="contentinfo"> <div id="f-poweredbyico"> <a href="//www.mediawiki.org/"><img src="/w/resources/assets/poweredby_mediawiki_88x31.png" alt="Powered by MediaWiki" srcset="/w/resources/assets/poweredby_mediawiki_132x47.png 1.5x, /w/resources/assets/poweredby_mediawiki_176x62.png 2x" width="88" height="31"/></a> </div> <ul id="f-list"> <li id="copyright">Content is available under <a href="/wiki/The_OEIS_End-User_License_Agreement" title="The OEIS End-User License Agreement">The OEIS End-User License Agreement</a> unless otherwise noted.</li> <li id="privacy"><a href="/wiki/OeisWiki:Privacy_policy" class="mw-redirect" title="OeisWiki:Privacy policy">License Agreements, Terms of Use, Privacy Policy</a></li> <li id="about"><a href="/wiki/OeisWiki:About" class="mw-redirect" title="OeisWiki:About">About OeisWiki</a></li> <li id="disclaimer"><a href="/wiki/OeisWiki:General_disclaimer" class="mw-redirect" title="OeisWiki:General disclaimer">Disclaimers</a></li> </ul> </div> </div> <script>(window.RLQ=window.RLQ||[]).push(function(){mw.config.set({"wgPageParseReport":{"limitreport":{"cputime":"0.216","walltime":"0.222","ppvisitednodes":{"value":3602,"limit":1000000},"ppgeneratednodes":{"value":8931,"limit":1000000},"postexpandincludesize":{"value":39277,"limit":2097152},"templateargumentsize":{"value":2862,"limit":2097152},"expansiondepth":{"value":20,"limit":40},"expensivefunctioncount":{"value":1,"limit":100},"timingprofile":["100.00% 208.713 1 Template:Sequence_of_the_Day/today","100.00% 208.713 1 -total"," 96.76% 201.954 1 Template:Sequence_of_the_Day_for_December_1"," 72.70% 151.731 7 Template:Math"," 63.97% 133.520 39 Template:Sp"," 14.34% 29.935 3 Template:^"," 11.28% 23.543 1 Template:SoD's_t_or_c"," 8.95% 18.673 4 Template:Mathfont"," 3.89% 8.123 3 Template:Op"," 3.31% 6.912 1 Template:Rel"]},"cachereport":{"timestamp":"20241201034344","ttl":3600,"transientcontent":true}}});});</script><script>(window.RLQ=window.RLQ||[]).push(function(){mw.config.set({"wgBackendResponseTime":615});});</script></body></html>