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A030984 - OEIS
<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 3.2 Final//EN"> <html> <head> <link rel="stylesheet" href="/styles.css"> <meta name="format-detection" content="telephone=no"> <meta http-equiv="content-type" content="text/html; charset=utf-8"> <meta name=viewport content="width=device-width, initial-scale=1"> <meta name="keywords" content="OEIS,integer sequences,Sloane" /> <title>A030984 - OEIS</title> <link rel="search" type="application/opensearchdescription+xml" title="OEIS" href="/oeis.xml"> <script> var myURL = "\/A030984" function redir() { var host = document.location.hostname; if(host != "oeis.org" && host != "127.0.0.1" && !/^([0-9.]+)$/.test(host) && host != "localhost" && host != "localhost.localdomain") { document.location = "https"+":"+"//"+"oeis"+".org/" + myURL; } } function sf() { if(document.location.pathname == "/" && document.f) document.f.q.focus(); } </script> </head> <body bgcolor=#ffffff onload="redir();sf()"> <div class=loginbar> <div class=login> <a href="/login?redirect=%2fA030984">login</a> </div> </div> <div class=center><div class=top> <center> <div class=donors> The OEIS is supported by <a href="http://oeisf.org/#DONATE">the many generous donors to the OEIS Foundation</a>. </div> <div class=banner> <a href="/"><img class=banner border="0" width="600" src="/banner2021.jpg" alt="A030984 - OEIS"></a> </div> </center> </div></div> <div class=center><div class=pagebody> <div class=searchbarcenter> <form name=f action="/search" method="GET"> <div class=searchbargreet> <div class=searchbar> <div class=searchq> <input class=searchbox maxLength=1024 name=q value="" title="Search Query"> </div> <div class=searchsubmit> <input type=submit value="Search" name=go> </div> <div class=hints> <span class=hints><a href="/hints.html">Hints</a></span> </div> </div> <div class=searchgreet> (Greetings from <a href="/welcome">The On-Line Encyclopedia of Integer Sequences</a>!) </div> </div> </form> </div> <div class=sequence> <div class=space1></div> <div class=line></div> <div class=seqhead> <div class=seqnumname> <div class=seqnum> A030984 </div> <div class=seqname> 2-automorphic numbers: final digits of 2*n^2 agree with n. </div> </div> <div class=scorerefs> 1 </div> </div> <div> <div class=seqdatabox> <div class=seqdata>8, 88, 688, 4688, 54688, 554688, 3554688, 93554688, 893554688, 893554688, 40893554688, 40893554688, 40893554688, 70040893554688, 870040893554688, 1870040893554688, 71870040893554688, 871870040893554688</div> <div class=seqdatalinks> (<a href="/A030984/list">list</a>; <a href="/A030984/graph">graph</a>; <a href="/search?q=A030984+-id:A030984">refs</a>; <a href="/A030984/listen">listen</a>; <a href="/history?seq=A030984">history</a>; <a href="/search?q=id:A030984&fmt=text">text</a>; <a href="/A030984/internal">internal format</a>) </div> </div> </div> <div class=entry> <div class=section> <div class=sectname>OFFSET</div> <div class=sectbody> <div class=sectline>1,1</div> </div> </div> <div class=section> <div class=sectname>COMMENTS</div> <div class=sectbody> <div class=sectline>a(n) is the unique positive integer less than 10^n such that a(n) is divisible by 2^n and 2*a(n) - 1 is divisible by 5^n. - <a href="/wiki/User:Eric_M._Schmidt">Eric M. Schmidt</a>, Aug 18 2012</div> </div> </div> <div class=section> <div class=sectname>LINKS</div> <div class=sectbody> <div class=sectline>Eric M. Schmidt, <a href="/A030984/b030984.txt">Table of n, a(n) for n = 1..1000</a></div> <div class=sectline>Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/AutomorphicNumber.html">Automorphic Number</a></div> <div class=sectline><a href="/index/Ar#automorphic">Index entries for sequences related to automorphic numbers</a></div> <div class=sectline><a href="/index/Fi#final">Index entries for sequences related to final digits of numbers</a></div> </div> </div> <div class=section> <div class=sectname>PROG</div> <div class=sectbody> <div class=sectline>(Sage) [crt(0, (5^n + 1)/2, 2^n, 5^n) for n in range(1, 1001)] # <a href="/wiki/User:Eric_M._Schmidt">Eric M. Schmidt</a>, Aug 18 2012</div> </div> </div> <div class=section> <div class=sectname>CROSSREFS</div> <div class=sectbody> <div class=sectline>Sequence in context: <a href="/A299749" title="Number of nX4 0..1 arrays with every element equal to 0, 1, 2, 3, 5, 6 or 8 king-move adjacent elements, with upper left ele...">A299749</a> <a href="/A300263" title="Number of nX4 0..1 arrays with every element equal to 0, 1, 2, 3, 5, 6, 7 or 8 king-move adjacent elements, with upper left ...">A300263</a> <a href="/A367278" title="Place n equally spaced points on each side of a square, and join each of these points by a chord to the 3*n new points on th...">A367278</a> * <a href="/A109021" title="(2*7^n - 6*3^n + 4)/6.">A109021</a> <a href="/A271939" title="Number of edges in the n-th order Sierpinski carpet graph.">A271939</a> <a href="/A043043" title="Base 10 palindromes that start with 8.">A043043</a></div> <div class=sectline>Adjacent sequences: <a href="/A030981" title="Number of noncrossing bushes with n nodes; i.e., rooted noncrossing trees with n nodes and no nonroot nodes of degree 1.">A030981</a> <a href="/A030982" title="Number of noncrossing nonplanted bushes with n nodes, i.e., rooted noncrossing trees with n nodes and no nodes of degree 1.">A030982</a> <a href="/A030983" title="Number of rooted noncrossing trees with n nodes such that root has degree 1 and the child of the root has degree at least 2.">A030983</a> * <a href="/A030985" title="3-automorphic numbers ending in 2: final digits of 3*n^2 agree with n.">A030985</a> <a href="/A030986" title="3-automorphic numbers ending in 5: final digits of 3*n^2 agree with n.">A030986</a> <a href="/A030987" title="4-automorphic numbers: final digits of 4*n^2 agree with n.">A030987</a></div> </div> </div> <div class=section> <div class=sectname>KEYWORD</div> <div class=sectbody> <div class=sectline><span title="a sequence of nonnegative numbers">nonn</span>,<span title="dependent on base used for sequence">base</span>,<span title="edited within the last two weeks">changed</span></div> </div> </div> <div class=section> <div class=sectname>AUTHOR</div> <div class=sectbody> <div class=sectline><a href="/wiki/User:Eric_W._Weisstein">Eric W. Weisstein</a></div> </div> </div> <div class=section> <div class=sectname>STATUS</div> <div class=sectbody> <div class=sectline>approved</div> </div> </div> </div> <div class=space10></div> </div> </div></div> <p> <div class=footerpad></div> <div class=footer> <center> <div class=bottom> <div class=linksbar> <a href="/">Lookup</a> <a href="/wiki/Welcome"><font color="red">Welcome</font></a> <a href="/wiki/Main_Page"><font color="red">Wiki</font></a> <a href="/wiki/Special:RequestAccount">Register</a> <a href="/play.html">Music</a> <a href="/plot2.html">Plot 2</a> <a href="/demo1.html">Demos</a> <a href="/wiki/Index_to_OEIS">Index</a> <a href="/webcam">WebCam</a> <a href="/Submit.html">Contribute</a> <a href="/eishelp2.html">Format</a> <a href="/wiki/Style_Sheet">Style Sheet</a> <a href="/transforms.html">Transforms</a> <a href="/ol.html">Superseeker</a> <a href="/recent">Recents</a> </div> <div class=linksbar> <a href="/community.html">The OEIS Community</a> </div> <div class=linksbar> Maintained by <a href="http://oeisf.org">The OEIS Foundation Inc.</a> </div> <div class=dbinfo>Last modified February 20 05:50 EST 2025. Contains 381032 sequences.</div> <div class=legal> <a href="/wiki/Legal_Documents">License Agreements, Terms of Use, Privacy Policy</a> </div> </div> </center> </div> </body> </html>