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A190876 - 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>A190876 - OEIS</title> <link rel="search" type="application/opensearchdescription+xml" title="OEIS" href="/oeis.xml"> <script> var myURL = "\/A190876" 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=%2fA190876">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="A190876 - 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> A190876 </div> <div class=seqname> Numbers 1 through 8 together with numbers congruent to 9 mod 10. </div> </div> <div class=scorerefs> 2 </div> </div> <div> <div class=seqdatabox> <div class=seqdata>1, 2, 3, 4, 5, 6, 7, 8, 9, 19, 29, 39, 49, 59, 69, 79, 89, 99, 109, 119, 129, 139, 149, 159, 169, 179, 189, 199, 209, 219, 229, 239, 249, 259, 269, 279, 289, 299, 309, 319, 329, 339, 349, 359, 369, 379, 389, 399, 409, 419, 429, 439, 449, 459, 469, 479, 489, 499, 509, 519, 529, 539, 549, 559, 569, 579, 589, 599, 609</div> <div class=seqdatalinks> (<a href="/A190876/list">list</a>; <a href="/A190876/graph">graph</a>; <a href="/search?q=A190876+-id:A190876">refs</a>; <a href="/A190876/listen">listen</a>; <a href="/history?seq=A190876">history</a>; <a href="/search?q=id:A190876&fmt=text">text</a>; <a href="/A190876/internal">internal format</a>) </div> </div> </div> <div class=entry> <div class=section> <div class=sectname>OFFSET</div> <div class=sectbody> <div class=sectline>1,2</div> </div> </div> <div class=section> <div class=sectname>COMMENTS</div> <div class=sectbody> <div class=sectline>In lunar arithmetic, numbers n with the property that the sum of the divisors of n that are <= n is equal to n.</div> </div> </div> <div class=section> <div class=sectname>LINKS</div> <div class=sectbody> <div class=sectline>Vincenzo Librandi, <a href="/A190876/b190876.txt">Table of n, a(n) for n = 1..1000</a></div> <div class=sectline>D. Applegate, M. LeBrun and N. J. A. Sloane, <a href="http://arxiv.org/abs/1107.1130">Dismal Arithmetic</a> [Note: we have now changed the name from "dismal arithmetic" to "lunar arithmetic" - the old name was too depressing]</div> <div class=sectline><a href="/index/Di#dismal">Index entries for sequences related to dismal (or lunar) arithmetic</a></div> <div class=sectline><a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).</div> </div> </div> <div class=section> <div class=sectname>FORMULA</div> <div class=sectbody> <div class=sectline>G.f.: x*(1+9*x^9)/(1-x)^2. - <a href="/wiki/User:Bruno_Berselli">Bruno Berselli</a>, May 23 2011</div> <div class=sectline>a(n) = 2*a(n-1) -a(n-2). - <a href="/wiki/User:Vincenzo_Librandi">Vincenzo Librandi</a>, Jul 12 2012</div> </div> </div> <div class=section> <div class=sectname>PROG</div> <div class=sectbody> <div class=sectline>(Maxima) makelist(if n<9 then n else 10*n-81, n, 1, 70); /* <a href="/wiki/User:Bruno_Berselli">Bruno Berselli</a>, May 24 2011 */</div> <div class=sectline>(Magma) [n lt 9 select n else 10*n-81: n in [1..70]]; // <a href="/wiki/User:Bruno_Berselli">Bruno Berselli</a>, May 24 2011</div> </div> </div> <div class=section> <div class=sectname>CROSSREFS</div> <div class=sectbody> <div class=sectline>Cf. <a href="/A017377" title="a(n) = 10*n + 9.">A017377</a>.</div> <div class=sectline>Sequence in context: <a href="/A088473" title="Numbers n such that the lunar sum of the distinct lunar prime divisors of n is <= n.">A088473</a> <a href="/A317110" title="Numbers k such that the smallest digit of k is equal to the additive digital root of k (in base 10).">A317110</a> <a href="/A340254" title="Lexicographically earliest sequence of distinct nonnegative terms such that for any n >= 0, a(n+1) is obtained by altering t...">A340254</a> * <a href="/A051885" title="Smallest number whose sum of digits is n.">A051885</a> <a href="/A227378" title="Smallest number with n = sum of distinct digits in decimal representation, cf. A217928.">A227378</a> <a href="/A226637" title="Numbers m having with m+1 no common digit in decimal representations.">A226637</a></div> <div class=sectline>Adjacent sequences: <a href="/A190873" title="a(n) = 12*a(n-1) - 12*a(n-2), a(0)=0, a(1)=1.">A190873</a> <a href="/A190874" title="First differences of A179196, pi(R_(n+1)) - pi(R_n) where R_n is A104272(n).">A190874</a> <a href="/A190875" title="E.g.f. exp(x+x^4)">A190875</a> * <a href="/A190877" title="Expansion of e.g.f. exp(x+x^5).">A190877</a> <a href="/A190878" title="E.g.f. exp(x/(1-x-x^4)).">A190878</a> <a href="/A190879" title="Numbers k having at least three distinct prime divisors and being divisible by the square of the sum of their prime divisors.">A190879</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></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>, May 23 2011</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 22 07:12 EST 2025. Contains 381098 sequences.</div> <div class=legal> <a href="/wiki/Legal_Documents">License Agreements, Terms of Use, Privacy Policy</a> </div> </div> </center> </div> </body> </html>