CINXE.COM
A018843 - 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>A018843 - OEIS</title> <link rel="search" type="application/opensearchdescription+xml" title="OEIS" href="/oeis.xml"> <script> var myURL = "\/A018843" 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=%2fA018843">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="A018843 - 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> A018843 </div> <div class=seqname> Number of n-dimensional unimodular lattices without roots. </div> </div> <div class=scorerefs> 0 </div> </div> <div> <div class=seqdatabox> <div class=seqdata>1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 1, 3, 38, 10092</div> <div class=seqdatalinks> (<a href="/A018843/list">list</a>; <a href="/A018843/graph">graph</a>; <a href="/search?q=A018843+-id:A018843">refs</a>; <a href="/A018843/listen">listen</a>; <a href="/history?seq=A018843">history</a>; <a href="/search?q=id:A018843&fmt=text">text</a>; <a href="/A018843/internal">internal format</a>) </div> </div> </div> <div class=entry> <div class=section> <div class=sectname>OFFSET</div> <div class=sectbody> <div class=sectline>0,25</div> </div> </div> <div class=section> <div class=sectname>COMMENTS</div> <div class=sectbody> <div class=sectline>The paper by Oliver King (king(AT)math.berkeley.edu) shows that a(29) >= 8900 and a(30) >= 82000000.</div> </div> </div> <div class=section> <div class=sectname>LINKS</div> <div class=sectbody> <div class=sectline><a href="/A018843/b018843.txt">Table of n, a(n) for n=0..29.</a></div> <div class=sectline>R. Bacher and B. B. Venkov, <a href="https://www-fourier.univ-grenoble-alpes.fr/?q=fr/content/reseaux-entiers-unimodulaires-sans-racine-en-dimension-27-et-28">R茅seaux entiers unimodulaires sans racine en dimension 27 et 28</a>, in R茅seaux euclidiens, designs sph茅riques et formes modulaires, pp. 212-267, Enseignement Math., Geneva, 2001.</div> <div class=sectline>Ga毛tan Chenevier, <a href="http://gaetan.chenevier.perso.math.cnrs.fr/pub.html">Publications</a></div> <div class=sectline>J. H. Conway and N. J. A. Sloane, <a href="https://www.researchgate.net/publication/46957856_Sphere_Packings_Lattices_and_Groups">Sphere Packings, Lattices and Groups</a>, Springer-Verlag, Preface to 3rd ed.</div> <div class=sectline>O. King, <a href="http://arXiv.org/abs/math/0012231">A mass formula for unimodular lattices with no roots</a>, arXiv:math/0012231 [math.NT], 2000-2001.</div> </div> </div> <div class=section> <div class=sectname>CROSSREFS</div> <div class=sectbody> <div class=sectline>Cf. <a href="/A005134" title="Number of n-dimensional unimodular lattices (or quadratic forms).">A005134</a>.</div> <div class=sectline>Sequence in context: <a href="/A271699" title="Triangle read by rows, T(n,k) = Sum_{j=0..n} (-1)^(n-j)*C(-j,-n)*S1(k,j), S1 the Stirling cycle numbers A132393, for n>=0 an...">A271699</a> <a href="/A216701" title="Decimal expansion of sqrt(2)/(2*log(2)).">A216701</a> <a href="/A278326" title="Decimal expansion of gamma/log(2)^2.">A278326</a> * <a href="/A152836" title="a(0)=-1; a(n)=n^a(n-1)-a(n-1)^n.">A152836</a> <a href="/A152837" title="a(0)=-1; a(n)=Floor[n^a(n-1)-a(n-1)^n].">A152837</a> <a href="/A182036" title="Expansion of q^(1/2) * eta(q^2)^2 * eta(q^6)^2 / (eta(q) * eta(q^9)^3) in powers of q.">A182036</a></div> <div class=sectline>Adjacent sequences: <a href="/A018840" title="Number of steps for {2,3} fairy knight to reach (n,0) on infinite chessboard.">A018840</a> <a href="/A018841" title="Number of steps for {2,3} fairy knight to reach (n,n) on infinite chessboard.">A018841</a> <a href="/A018842" title="Number of squares on infinite chessboard at n knight's moves from center.">A018842</a> * <a href="/A018844" title="Arises from generalized Lucas-Lehmer test for primality.">A018844</a> <a href="/A018845" title="Number of iterations required for the sum of n and its prime divisors = t to reach a prime (where t replaces n in each itera...">A018845</a> <a href="/A018846" title="Strobogrammatic numbers: numbers that are the same upside down (using calculator-style numerals).">A018846</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="next term not known, may be hard to find. please extend this sequence">hard</span></div> </div> </div> <div class=section> <div class=sectname>AUTHOR</div> <div class=sectbody> <div class=sectline><a href="/wiki/User:N._J._A._Sloane">N. J. A. Sloane</a>, <a href="/wiki/User:Roland_Bacher">Roland Bacher</a></div> </div> </div> <div class=section> <div class=sectname>EXTENSIONS</div> <div class=sectbody> <div class=sectline>a(29) added from Ga毛tan Chenevier's page by <a href="/wiki/User:Andrey_Zabolotskiy">Andrey Zabolotskiy</a>, Nov 02 2021</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 April 9 00:10 EDT 2025. Contains 382608 sequences.</div> <div class=legal> <a href="/wiki/Legal_Documents">License Agreements, Terms of Use, Privacy Policy</a> </div> </div> </center> </div> </body> </html>