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mw-hide-empty-elt ns-2 ns-subject page-User_Charles_R_Greathouse_IV rootpage-User_Charles_R_Greathouse_IV 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">User:Charles R Greathouse IV</h1> <div id="bodyContent" class="mw-body-content"> <div id="siteSub">From OeisWiki</div> <div id="contentSub"></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"><p><a href="/wiki/Editorial_Board" title="Editorial Board">Editor-in-Chief</a>, interested primarily in computational number theory and allied fields. </p><p>I can be contacted via my Talk page here, or by <a href="/wiki/Special:EmailUser/Charles_R_Greathouse_IV" title="Special:EmailUser/Charles R Greathouse IV">email</a>. </p> <table> <tr> <td> <a href="/wiki/User:Charles_R_Greathouse_IV/Averages" title="User:Charles R Greathouse IV/Averages">User:Charles R Greathouse IV/Averages</a> </td> <td> Early draft of an article. </td></tr> <tr> <td> <a href="/wiki/User:Charles_R_Greathouse_IV/Chase_sequences" title="User:Charles R Greathouse IV/Chase sequences">User:Charles R Greathouse IV/Chase sequences</a> </td> <td> 'Chase sequences': Axxxxxx refers to Ayyyyyy, which refers to Azzzzzz... </td></tr> <tr> <td> <a href="/wiki/User:Charles_R_Greathouse_IV/Favorites" title="User:Charles R Greathouse IV/Favorites">User:Charles R Greathouse IV/Favorites</a> </td> <td> Some of my favorite sequences. </td></tr> <tr> <td> <a href="/wiki/User:Charles_R_Greathouse_IV/Format" title="User:Charles R Greathouse IV/Format">User:Charles R Greathouse IV/Format</a> </td> <td> Discusses the correct format of b-files and how to repair ill-formatted b-files. </td></tr> <tr> <td> <a href="/wiki/User:Charles_R_Greathouse_IV/Junk" title="User:Charles R Greathouse IV/Junk">User:Charles R Greathouse IV/Junk</a> </td> <td> Disreputable publishers, journals, etc. </td></tr> <tr> <td> <a href="/wiki/User:Charles_R_Greathouse_IV/Keywords" title="User:Charles R Greathouse IV/Keywords">User:Charles R Greathouse IV/Keywords</a> </td> <td> Information on keywords: when to use them, new ones to add, etc. </td></tr> <tr> <td> <a href="/wiki/User:Charles_R_Greathouse_IV/Metadata" title="User:Charles R Greathouse IV/Metadata">User:Charles R Greathouse IV/Metadata</a> </td> <td> Plans for OEIS metadata: keywords, categories, the index, etc. </td></tr> <tr> <td> <a href="/wiki/User:Charles_R_Greathouse_IV/Pari" title="User:Charles R Greathouse IV/Pari">User:Charles R Greathouse IV/Pari</a> </td> <td> Some PARI/GP tools. </td></tr> <tr> <td> <a href="/wiki/User:Charles_R_Greathouse_IV/Programs" title="User:Charles R Greathouse IV/Programs">User:Charles R Greathouse IV/Programs</a> </td> <td> Programs in the OEIS: types, format, etc. </td></tr> <tr> <td> <a href="/wiki/User:Charles_R_Greathouse_IV/Projects" title="User:Charles R Greathouse IV/Projects">User:Charles R Greathouse IV/Projects</a> </td> <td> Other mathematical databases, fingerprint databases, and similar projects </td></tr> <tr> <td> <a href="/wiki/User:Charles_R_Greathouse_IV/Properties" title="User:Charles R Greathouse IV/Properties">User:Charles R Greathouse IV/Properties</a> </td> <td> Sequence properties and classes </td></tr> <tr> <td> <a href="/wiki/User:Charles_R_Greathouse_IV/Rule_of_thumb" title="User:Charles R Greathouse IV/Rule of thumb">User:Charles R Greathouse IV/Rule of thumb</a> </td> <td> Sequences should take 1 hour to prepare for submission. </td></tr> <tr> <td> <a href="/wiki/User:Charles_R_Greathouse_IV/Standards" title="User:Charles R Greathouse IV/Standards">User:Charles R Greathouse IV/Standards</a> </td> <td> How to write up certain kinds of sequences. </td></tr> <tr> <td> <a href="/wiki/User:Charles_R_Greathouse_IV/Tables_of_special_primes" title="User:Charles R Greathouse IV/Tables of special primes">User:Charles R Greathouse IV/Tables of special primes</a> </td> <td> Types of primes and their densities </td></tr> <tr> <td> <a href="/wiki/User:Charles_R_Greathouse_IV/To_do" title="User:Charles R Greathouse IV/To do">User:Charles R Greathouse IV/To do</a> </td> <td> Sequences to work on and b-files to fix. </td></tr> <tr> <td> <a href="/wiki/User:Charles_R_Greathouse_IV/Vanity" title="User:Charles R Greathouse IV/Vanity">User:Charles R Greathouse IV/Vanity</a> </td> <td> Sequences named after their discoverer. </td></tr> <tr> <td> <a href="/wiki/User:Charles_R_Greathouse_IV/Wiki" title="User:Charles R Greathouse IV/Wiki">User:Charles R Greathouse IV/Wiki</a> </td> <td> Tools for the OEIS wiki. </td></tr> </table> <p>Projects: </p> <ul><li><a href="/wiki/Historical_sequences" title="Historical sequences">Historical sequences</a></li> <li><a href="/wiki/The_multi-faceted_reach_of_the_OEIS" title="The multi-faceted reach of the OEIS">The multi-faceted reach of the OEIS</a></li> <li><a href="/wiki/Sequences_determined_by_prime_signature" title="Sequences determined by prime signature">Sequences determined by prime signature</a></li></ul> <p>Useful links: </p> <ul><li><a href="/wiki/Features_Wishlist" title="Features Wishlist">Features Wishlist</a>, <a href="/wiki/User:Russ_Cox/OEIS_Server_Features" title="User:Russ Cox/OEIS Server Features">User:Russ Cox/OEIS Server Features</a>, <a href="/wiki/Suggested_Projects" title="Suggested Projects">Suggested Projects</a></li> <li><a href="/wiki/Deleted_sequences" title="Deleted sequences">Deleted sequences</a> (<a rel="nofollow" class="external text" href="https://oeis.org/w/index.php?title=Deleted_sequences&action=edit&section=4">most recent month</a>)</li> <li><a href="/wiki/Suggested_pre-submit_checklist" title="Suggested pre-submit checklist">Suggested pre-submit checklist</a></li> <li><a href="/wiki/Requested_articles" title="Requested articles">Requested articles</a></li> <li>Editing history: <a rel="nofollow" class="external text" href="http://oeis.org/history?user=Charles%20R%20Greathouse%20IV">sequence</a>, <a href="/wiki/Special:Contributions/Charles_R_Greathouse_IV" title="Special:Contributions/Charles R Greathouse IV">wiki</a></li> <li> References on proof attempts: <a rel="nofollow" class="external text" href="http://www.win.tue.nl/~gwoegi/P-versus-NP.htm">P vs. NP</a>, <a rel="nofollow" class="external text" href="http://empslocal.ex.ac.uk/people/staff/mrwatkin/zeta/RHproofs.htm">Riemann hypothesis</a></li> <li> Resources: <a rel="nofollow" class="external text" href="http://iml.univ-mrs.fr/~ramare/TME-EMT/accueil.html">TME-EMT</a></li></ul> <p><br /> </p> <table style="margin: 0.25em auto; font-size: 1.5em;"><tr><td><a href="/wiki/Template:Sequence_of_the_Day" title="Template:Sequence of the Day">Sequence of the Day</a></td></tr></table><br /> <div style="float: right; clear: both; margin-top: 0.75em;">[<a href="/w/index.php?title=Template_talk:Sequence_of_the_Day_for_November_24&action=edit&redlink=1" class="new" title="Template talk:Sequence of the Day for November 24 (page does not exist)">talk</a>]</div> <h2><span class="mw-headline" id="Sequence_of_the_Day_for_November_24"><a href="/wiki/Template:Sequence_of_the_Day_for_November_24" title="Template:Sequence of the Day for November 24">Sequence of the Day for November 24</a></span></h2> <a href="http://oeis.org/A000055">A000055</a>: Number of trees with <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,\, n \ge 0, }"><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>n</i>   ≥   0,</td></tr></table></span></span> unlabeled nodes. <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';">{ 1, 1, 1, 1, 2, 3, 6, 11, 23, 47, 106, 235, ... }</div></div></dd></dl> <table class="wikitable" cellspacing="0" cellpadding="0" style="margin: auto; border-collapse: collapse; border: 1px solid darkgray; background: #f9f9f9; color: black; empty-cells: show; text-align: center;"> <caption> Trees with <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> unlabeled nodes<sup id="cite_ref-1" class="reference"><a href="#cite_note-1">[1]</a></sup> <p></caption> </p> <tr style="background: #f2f2f2; color: black;"> <th style="width: 25px;"> <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> </th> <th> Trees </th></tr> <tr> <td> <b>0</b> </td> <td> <pre style="text-align: left;"> </pre>Null tree </td></tr> <tr> <td> <b>1</b> </td> <td> <pre style="text-align: left;">●</pre> </td></tr> <tr> <td> <b>2</b> </td> <td> <pre style="text-align: left;">●—●</pre> </td></tr> <tr> <td> <b>3</b> </td> <td> <pre style="text-align: left;">●—●—●</pre> </td></tr> <tr> <td> <b>4</b> </td> <td> <pre style="text-align: left;"> ● / ●—●—●—● ●—● \ ● </pre> </td></tr> <tr> <td> <b>5</b> </td> <td> <pre style="text-align: left;"> ● ● / | ●—●—●—●—● ●—●—● ●—●—● \ | ● ● </pre> </td></tr> </table> <p>This is the sequence for the example search on the front page of the <a href="/wiki/OEIS" class="mw-redirect" title="OEIS">OEIS</a>. This Thanksgiving we are thankful for, among other things, the OEIS, which is an invaluable resource in many mathematical and scientific endeavors. </p><p>__________ </p> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><a href="#cite_ref-1">↑</a></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://mathworld.wolfram.com/about/author.html">Weisstein, Eric W.</a>, <a rel="nofollow" class="external text" href="http://mathworld.wolfram.com/Tree.html">Tree</a>, from MathWorld—A Wolfram Web Resource.</span> </li> </ol></div> <p><br /> </p> <h2><span class="mw-headline" id="Sequences_in_the_News">Sequences in the News</span></h2> <ul><li> <b>Aug 17 2021</b> Swiss scientists announce they have calculated π (<a href="http://oeis.org/A000796">A000796</a>) to 62.8 trillion digits in only 108 days.</li> <li> <b>Dec 25 2018</b> German Heise-News "integers, please" column explains <a href="http://oeis.org/A003173">A003173</a> and OEIS. </li> <li> <b>Feb 01 2018</b> Alphabet announced a $8,589,869,056 = $<a href="http://oeis.org/A000396">A000396</a>(6) stock buyback.</li> <li> <b>Jan 03 2018</b> Largest known term of <a href="http://oeis.org/A000043">A000043</a> announced: 77232917.</li> <li> <b>Nov 18 2016</b> PrimeGrid proves that 10223 is not a Sierpinski number, since 10223 × 2<span style="position: relative; vertical-align: 1.25ex; line-height: 0.75ex; font-size: 0.75em;"><span style="position: relative; vertical-align: middle;"> 31172165</span></span> + 1 is prime. So no changes to <a href="http://oeis.org/A076336">A076336</a> for now.</li> <li> <b>Sep 14 2016</b> Tom Greer discovers the twin primes 2996863034895 × 2<span style="position: relative; vertical-align: 1.25ex; line-height: 0.75ex; font-size: 0.75em;"><span style="position: relative; vertical-align: middle;"> 1290000</span></span> ± 1 using PrimeGrid, TwinGen and LLR.</li> <li> <b>Jan 19 2016</b> Largest known term of <a href="http://oeis.org/A000043">A000043</a> announced: 74207281, also discovered by Curtis Cooper.</li></ul> <p><br /> </p> <h2><span class="mw-headline" id="Complaints">Complaints</span></h2> <p>I strive to live up to the highest ethical standards. If you feel that I have wrongly rejected one of your sequences (or otherwise failed to meet the expected standards), please leave a note at <a href="/wiki/Complaints_About_Editing" title="Complaints About Editing">Complaints About Editing</a> where it will be reviewed. I hope that in all cases you will first contact me (through the pink comment boxes, on my <a href="/wiki/User_talk:Charles_R_Greathouse_IV" title="User talk:Charles R Greathouse IV">user page</a>, or by email). </p>   </div>  </div><div class="printfooter"> Retrieved from "<a dir="ltr" href="https://oeis.org/w/index.php?title=User:Charles_R_Greathouse_IV&oldid=1651556">https://oeis.org/w/index.php?title=User:Charles_R_Greathouse_IV&oldid=1651556</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-user" class="selected"><a href="/wiki/User:Charles_R_Greathouse_IV" title="View the user page [c]" accesskey="c">User page</a></li> <li id="ca-talk"><a href="/wiki/User_talk:Charles_R_Greathouse_IV" rel="discussion" title="Discussion about the content page [t]" accesskey="t">Discussion</a></li> <li id="ca-viewsource"><a href="/w/index.php?title=User:Charles_R_Greathouse_IV&action=edit" title="This page is protected.
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