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A317110 - 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>A317110 - OEIS</title> <link rel="search" type="application/opensearchdescription+xml" title="OEIS" href="/oeis.xml"> <script> var myURL = "\/A317110" 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=%2fA317110">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="A317110 - 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> A317110 </div> <div class=seqname> Numbers k such that the smallest digit of k is equal to the additive digital root of k (in base 10). </div> </div> <div class=scorerefs> 0 </div> </div> <div> <div class=seqdatabox> <div class=seqdata>0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 19, 29, 39, 49, 59, 69, 79, 89, 91, 92, 93, 94, 95, 96, 97, 98, 99, 118, 127, 136, 145, 154, 163, 172, 181, 199, 217, 227, 236, 245, 254, 263, 271, 272, 299, 316, 326, 336, 345, 354, 361, 362, 363, 399, 415, 425, 435, 445, 451</div> <div class=seqdatalinks> (<a href="/A317110/list">list</a>; <a href="/A317110/graph">graph</a>; <a href="/search?q=A317110+-id:A317110">refs</a>; <a href="/A317110/listen">listen</a>; <a href="/history?seq=A317110">history</a>; <a href="/search?q=id:A317110&fmt=text">text</a>; <a href="/A317110/internal">internal format</a>) </div> </div> </div> <div class=entry> <div class=section> <div class=sectname>OFFSET</div> <div class=sectbody> <div class=sectline>1,3</div> </div> </div> <div class=section> <div class=sectname>COMMENTS</div> <div class=sectbody> <div class=sectline>Numbers k such that <a href="/A054054" title="Smallest digit of n.">A054054</a>(k) = <a href="/A010888" title="Digital root of n (repeatedly add the digits of n until a single digit is reached).">A010888</a>(k).</div> </div> </div> <div class=section> <div class=sectname>LINKS</div> <div class=sectbody> <div class=sectline><a href="/A317110/b317110.txt">Table of n, a(n) for n=1..59.</a></div> <div class=sectline>Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/DigitalRoot.html">Digital Root</a></div> </div> </div> <div class=section> <div class=sectname>MATHEMATICA</div> <div class=sectbody> <div class=sectline>Select[Range@ 451, Min@ IntegerDigits@ # == FixedPoint[Total@ IntegerDigits@ # &, #] &] (* <a href="/wiki/User:Michael_De_Vlieger">Michael De Vlieger</a>, Jul 22 2018 *)</div> </div> </div> <div class=section> <div class=sectname>PROG</div> <div class=sectbody> <div class=sectline>(Magma) [n : n in [1..10000] | (1+(n-1) mod 9) eq &+[Min(Intseq(n))]];</div> <div class=sectline>(PARI) isok(n) = (n==0) || (vecmin(digits(n)) == (n-1)%9+1); \\ <a href="/wiki/User:Michel_Marcus">Michel Marcus</a>, Jul 23 2018</div> </div> </div> <div class=section> <div class=sectname>CROSSREFS</div> <div class=sectbody> <div class=sectline>Cf. <a href="/A010888" title="Digital root of n (repeatedly add the digits of n until a single digit is reached).">A010888</a>, <a href="/A054054" title="Smallest digit of n.">A054054</a>, <a href="/A107085" title="Numbers n such that in decimal representation the largest digit is equal to the digital root.">A107085</a> (with "largest" digit instead of "smallest").</div> <div class=sectline>Sequence in context: <a href="/A075517" title="Created by removing all integers which take an odd number of nested digit sums to reach <10.">A075517</a> <a href="/A248013" title="Numbers m such that A247796(m) = m.">A248013</a> <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="/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="/A190876" title="Numbers 1 through 8 together with numbers congruent to 9 mod 10.">A190876</a> <a href="/A051885" title="Smallest number whose sum of digits is n.">A051885</a></div> <div class=sectline>Adjacent sequences: <a href="/A317107" title="Numbers missing from A317105.">A317107</a> <a href="/A317108" title="Numbers missing from A317106.">A317108</a> <a href="/A317109" title="a(n) is the total number of edges after n-th stage in the diagram of the symmetries of sigma described in A236104, with a(0)...">A317109</a> * <a href="/A317111" title="Number of permutations of [n] in which the length of every increasing run is 0 or 1 (mod 4).">A317111</a> <a href="/A317112" title="Number of nXn 0..1 arrays with every element unequal to 0, 1, 2, 3, 4, 7 or 8 king-move adjacent elements, with upper left e...">A317112</a> <a href="/A317113" title="Number of nX3 0..1 arrays with every element unequal to 0, 1, 2, 3, 4, 7 or 8 king-move adjacent elements, with upper left e...">A317113</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:Jaroslav_Krizek">Jaroslav Krizek</a>, Jul 21 2018</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 20:12 EST 2025. Contains 381121 sequences.</div> <div class=legal> <a href="/wiki/Legal_Documents">License Agreements, Terms of Use, Privacy Policy</a> </div> </div> </center> </div> </body> </html>