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A118598 - 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>A118598 - OEIS</title> <link rel="search" type="application/opensearchdescription+xml" title="OEIS" href="/oeis.xml"> <script> var myURL = "\/A118598" 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=%2fA118598">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="A118598 - OEIS"></a> </div> <div class="motdbox"> <div class="motd"> <p>Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).</p> </div> <div class="donate"> <div id="donate-button-container"> <div id="donate-button"></div> <script src="https://www.paypalobjects.com/donate/sdk/donate-sdk.js" charset="UTF-8"></script> <script> PayPal.Donation.Button({ env:'production', hosted_button_id:'SVPGSDDCJ734A', image: { src:'https://www.paypalobjects.com/en_US/i/btn/btn_donateCC_LG.gif', alt:'Donate with PayPal button', title:'PayPal - The safer, easier way to pay online!', } }).render('#donate-button'); </script> </div> <a href="https://oeisf.org/donate/"> <strong>Other ways to Give</strong> </a> </div> </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> A118598 </div> <div class=seqname> Palindromes in base 7 (written in base 7). </div> </div> <div class=scorerefs> 10 </div> </div> <div> <div class=seqdatabox> <div class=seqdata>0, 1, 2, 3, 4, 5, 6, 11, 22, 33, 44, 55, 66, 101, 111, 121, 131, 141, 151, 161, 202, 212, 222, 232, 242, 252, 262, 303, 313, 323, 333, 343, 353, 363, 404, 414, 424, 434, 444, 454, 464, 505, 515, 525, 535, 545, 555, 565, 606, 616, 626, 636, 646, 656, 666, 1001</div> <div class=seqdatalinks> (<a href="/A118598/list">list</a>; <a href="/A118598/graph">graph</a>; <a href="/search?q=A118598+-id:A118598">refs</a>; <a href="/A118598/listen">listen</a>; <a href="/history?seq=A118598">history</a>; <a href="/search?q=id:A118598&fmt=text">text</a>; <a href="/A118598/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>LINKS</div> <div class=sectbody> <div class=sectline><a href="/A118598/b118598.txt">Table of n, a(n) for n=1..56.</a></div> </div> </div> <div class=section> <div class=sectname>MATHEMATICA</div> <div class=sectbody> <div class=sectline>(* get NextPalindrome from <a href="/A029965" title="Palindromic in bases 9 and 10.">A029965</a> *) Select[NestList[NextPalindrome, 0, 109], Max@IntegerDigits@# < 7 &] (* <a href="/wiki/User:Robert_G._Wilson_v">Robert G. Wilson v</a>, May 09 2006 *)</div> </div> </div> <div class=section> <div class=sectname>PROG</div> <div class=sectbody> <div class=sectline>(Python)</div> <div class=sectline>from sympy import integer_log</div> <div class=sectline>from gmpy2 import digits</div> <div class=sectline>def <a href="/A118598" title="Palindromes in base 7 (written in base 7).">A118598</a>(n):</div> <div class=sectline> if n == 1: return 0</div> <div class=sectline> y = 7*(x:=7**integer_log(n>>1, 7)[0])</div> <div class=sectline> return int((s:=digits(n-x, 7))+s[-2::-1] if n<x+y else (s:=digits(n-y, 7))+s[::-1]) # <a href="/wiki/User:Chai_Wah_Wu">Chai Wah Wu</a>, Jun 14 2024</div> </div> </div> <div class=section> <div class=sectname>CROSSREFS</div> <div class=sectbody> <div class=sectline>Cf. <a href="/A029954" title="Palindromic in base 7.">A029954</a>, <a href="/A057148" title="Palindromes only using 0 and 1 (i.e., base-2 palindromes).">A057148</a>, <a href="/A118594" title="Palindromes in base 3 (written in base 3).">A118594</a>, <a href="/A118595" title="Palindromes in base 4 (written in base 4).">A118595</a>, <a href="/A118596" title="Palindromes in base 5 (written in base 5).">A118596</a>, <a href="/A118597" title="Palindromes in base 6 (written in base 6).">A118597</a>, <a href="/A118598" title="Palindromes in base 7 (written in base 7).">A118598</a>, <a href="/A118599" title="Palindromes in base 8 (written in base 8).">A118599</a>, <a href="/A118600" title="Palindromes in base 9 (written in base 9).">A118600</a>, <a href="/A002113" title="Palindromes in base 10.">A002113</a>.</div> <div class=sectline>Sequence in context: <a href="/A060733" title="a(n) = a(n-1) + a(n - 1 minus the number of terms of a(k) == (mod 6) so far).">A060733</a> <a href="/A283563" title="Numbers n such that A112368(n) = Sum_{i=0..n} 2^i*i! is prime.">A283563</a> <a href="/A033078" title="Numbers in which all pairs of consecutive base-7 digits differ by 3.">A033078</a> * <a href="/A264976" title="Permutation of nonnegative integers: a(n) = A263272(A264974(n)).">A264976</a> <a href="/A243286" title="Self-inverse permutation of natural numbers induced by the restriction of A243057 (or A243059 or A242420) to the union of {1...">A243286</a> <a href="/A113006" title="A113001(A113001(n)).">A113006</a></div> <div class=sectline>Adjacent sequences: <a href="/A118595" title="Palindromes in base 4 (written in base 4).">A118595</a> <a href="/A118596" title="Palindromes in base 5 (written in base 5).">A118596</a> <a href="/A118597" title="Palindromes in base 6 (written in base 6).">A118597</a> * <a href="/A118599" title="Palindromes in base 8 (written in base 8).">A118599</a> <a href="/A118600" title="Palindromes in base 9 (written in base 9).">A118600</a> <a href="/A118601" title="Partial sums of A058129.">A118601</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:Martin_Renner">Martin Renner</a>, May 08 2006</div> </div> </div> <div class=section> <div class=sectname>EXTENSIONS</div> <div class=sectbody> <div class=sectline>Corrected and extended by <a href="/wiki/User:Robert_G._Wilson_v">Robert G. Wilson v</a>, May 09 2006</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 December 11 06:39 EST 2024. Contains 378604 sequences.</div> <div class=legal> <a href="/wiki/Legal_Documents">License Agreements, Terms of Use, Privacy Policy</a> </div> </div> </center> </div> </body> </html>