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A060731 - 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>A060731 - OEIS</title> <link rel="search" type="application/opensearchdescription+xml" title="OEIS" href="/oeis.xml"> <script> var myURL = "\/A060731" 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=%2fA060731">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="A060731 - 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> A060731 </div> <div class=seqname> a(n) = a(n-1) + a(n - 1 minus the number of terms of a(k) == (mod 4) so far). </div> </div> <div class=scorerefs> 0 </div> </div> <div> <div class=seqdatabox> <div class=seqdata>1, 2, 3, 4, 7, 11, 14, 25, 36, 50, 64, 89, 125, 175, 225, 314, 378, 467, 592, 817, 992, 1306, 1684, 2062, 2529, 2996, 3988, 4580, 5572, 6878, 9407, 10399, 12928, 15457, 19445, 21507, 25495, 31067, 35647, 40227, 49634, 60033, 66911, 77310, 92767</div> <div class=seqdatalinks> (<a href="/A060731/list">list</a>; <a href="/A060731/graph">graph</a>; <a href="/search?q=A060731+-id:A060731">refs</a>; <a href="/A060731/listen">listen</a>; <a href="/history?seq=A060731">history</a>; <a href="/search?q=id:A060731&fmt=text">text</a>; <a href="/A060731/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>LINKS</div> <div class=sectbody> <div class=sectline><a href="/A060731/b060731.txt">Table of n, a(n) for n=1..45.</a></div> </div> </div> <div class=section> <div class=sectname>EXAMPLE</div> <div class=sectbody> <div class=sectline>a(5) = a(4) + a(4 - the number of terms congruent to 1 (mod 4) so far) = a(4) + a(4-1) = 4 + 3 = 7.</div> </div> </div> <div class=section> <div class=sectname>MATHEMATICA</div> <div class=sectbody> <div class=sectline>m[ 1 ] = 1; m[ 2 ] = 2; m[ 3 ] = 3; a[ 4 ] = 4; m[ n_Integer ] := m[ n ] = Block[ {a = b = c = d = 0}, Do[ Switch[ Mod[ m[ k ], 4 ], 0, a++, 1, b++, 2, c++, 3, d++ ], {k, 1, n - 1} ]; Switch[ Mod[ n, 4 ], 0, m[ n - 1 ] + m[ n - 1 - a ], 1, m[ n - 1 ] + m[ n - 1 - b ], 2, m[ n - 1 ] + m[ n - 1 - c ], 3, m[ n - 1 ] + m[ n - 1 - d ] ] ]; Table[ m[ n ], {n, 1, 50} ]</div> </div> </div> <div class=section> <div class=sectname>CROSSREFS</div> <div class=sectbody> <div class=sectline>Sequence in context: <a href="/A171027" title="In the sequence of prime numbers, replace all the '5' digits with '4' and vice versa.">A171027</a> <a href="/A348792" title="Numbers k such that the reverse concatenation of the first k binary numbers A098780(k) is prime.">A348792</a> <a href="/A064933" title="Numbers k such that the period of the continued fraction for sqrt(3)*k is 2.">A064933</a> * <a href="/A238492" title="Number of partitions of n not containing 4*(number of parts) as a part.">A238492</a> <a href="/A140827" title="Interleave denominators and numerators of convergents to sqrt(3).">A140827</a> <a href="/A125621" title="Minimal number of blocks in any disjunct (n,3)-splitting system.">A125621</a></div> <div class=sectline>Adjacent sequences: <a href="/A060728" title="Numbers n such that Ramanujan's equation x^2 + 7 = 2^n has an integer solution.">A060728</a> <a href="/A060729" title="a(n+1) = a(n) + a(n minus the number of terms of the same parity as n so far).">A060729</a> <a href="/A060730" title="a(n) = a(n-1) + a(n - 1 minus the number of terms of a(k) == n (mod 3) so far).">A060730</a> * <a href="/A060732" title="a(n) = a(n-1) + a(n - 1 minus the number of terms of a(k) == (mod 5) so far).">A060732</a> <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="/A060734" title="Natural numbers written as a square array ending in last row from left to right and rightmost column from bottom to top are ...">A060734</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></div> </div> </div> <div class=section> <div class=sectname>AUTHOR</div> <div class=sectbody> <div class=sectline><a href="/wiki/User:Robert_G._Wilson_v">Robert G. Wilson v</a>, Apr 22 2001</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 January 21 02:28 EST 2025. Contains 380086 sequences.</div> <div class=legal> <a href="/wiki/Legal_Documents">License Agreements, Terms of Use, Privacy Policy</a> </div> </div> </center> </div> </body> </html>