CINXE.COM
A029987 - 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>A029987 - OEIS</title> <link rel="search" type="application/opensearchdescription+xml" title="OEIS" href="/oeis.xml"> <script> var myURL = "\/A029987" 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=%2fA029987">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="A029987 - 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> A029987 </div> <div class=seqname> Squares which are palindromes in base 4. </div> </div> <div class=scorerefs> 14 </div> </div> <div> <div class=seqdatabox> <div class=seqdata>0, 1, 25, 289, 441, 4225, 5041, 6889, 66049, 74529, 78961, 100489, 1050625, 1113025, 16785409, 17313921, 17581249, 19368801, 26594649, 26822041, 27258841, 268468225, 272613121, 284428225, 297183121, 4295098369</div> <div class=seqdatalinks> (<a href="/A029987/list">list</a>; <a href="/A029987/graph">graph</a>; <a href="/search?q=A029987+-id:A029987">refs</a>; <a href="/A029987/listen">listen</a>; <a href="/history?seq=A029987">history</a>; <a href="/search?q=id:A029987&fmt=text">text</a>; <a href="/A029987/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>Chai Wah Wu, <a href="/A029987/b029987.txt">Table of n, a(n) for n = 1..408</a></div> <div class=sectline>Patrick De Geest, <a href="https://www.worldofnumbers.com/nobase10pg2.htm">Palindromic Squares in bases 2 to 17</a></div> </div> </div> <div class=section> <div class=sectname>EXAMPLE</div> <div class=sectbody> <div class=sectline>5^2 = 25 in base 4 is 121, which is a palindrome, hence 25 is in the sequence.</div> <div class=sectline>6^2 = 36 in base 4 is 210, which is not a palindrome, so 36 is not in the sequence.</div> </div> </div> <div class=section> <div class=sectname>MATHEMATICA</div> <div class=sectbody> <div class=sectline>palindromicQ[n_, b_:10] := TrueQ[IntegerDigits[n, b] == Reverse[IntegerDigits[n, b]]]; Select[Range[1000]^2, palindromicQ[#, 4] &] (* <a href="/wiki/User:Alonso_del_Arte">Alonso del Arte</a>, Mar 04 2017 *)</div> <div class=sectline>Select[Range[0, 70000]^2, IntegerDigits[#, 4]==Reverse[IntegerDigits[#, 4]]&] (* <a href="/wiki/User:Harvey_P._Dale">Harvey P. Dale</a>, May 07 2022 *)</div> </div> </div> <div class=section> <div class=sectname>PROG</div> <div class=sectbody> <div class=sectline>(PARI) lista(nn) = for (n=0, nn, d = digits(n^2, 4); if (Vecrev(d) == d, print1(n^2, ", "))); \\ <a href="/wiki/User:Michel_Marcus">Michel Marcus</a>, Mar 05 2017</div> </div> </div> <div class=section> <div class=sectname>CROSSREFS</div> <div class=sectbody> <div class=sectline>Cf. <a href="/A029986" title="Numbers k such that k^2 is palindromic in base 4.">A029986</a>.</div> <div class=sectline>Sequence in context: <a href="/A265967" title="Number of nX2 0..4 arrays with the absolute differences of each element with its with horizontal and vertical neighbors unique.">A265967</a> <a href="/A225873" title="Squares that become prime when their most significant (or leftmost) digit is removed.">A225873</a> <a href="/A351925" title="Squares which are the concatenation of two primes.">A351925</a> * <a href="/A017582" title="a(n) = (12n + 5)^2.">A017582</a> <a href="/A335598" title="Squares that remain squares when the repunit with the same number of digits is added.">A335598</a> <a href="/A210430" title="Number of semistandard Young tableaux over all partitions of 8 with maximal element <= n.">A210430</a></div> <div class=sectline>Adjacent sequences: <a href="/A029984" title="Numbers k such that k^2 is palindromic in base 3.">A029984</a> <a href="/A029985" title="Squares which are palindromes in base 3.">A029985</a> <a href="/A029986" title="Numbers k such that k^2 is palindromic in base 4.">A029986</a> * <a href="/A029988" title="Numbers k such that k^2 is palindromic in base 5.">A029988</a> <a href="/A029989" title="Squares which are palindromes in base 5.">A029989</a> <a href="/A029990" title="Numbers k such that k^2 is palindromic in base 6.">A029990</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:Patrick_De_Geest">Patrick De Geest</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 April 9 16:10 EDT 2025. Contains 382627 sequences.</div> <div class=legal> <a href="/wiki/Legal_Documents">License Agreements, Terms of Use, Privacy Policy</a> </div> </div> </center> </div> </body> </html>