keyword:new

<!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>keyword:new - OEIS</title> <link rel="search" type="application/opensearchdescription+xml" title="OEIS" href="/oeis.xml"> <script> var myURL = "\/search?q=keyword:new\u0026sort=created" 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=%2fsearch%3fq%3dkeyword%3anew%26sort%3dcreated">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="keyword:new - 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="keyword:new" title="Search Query"> <input type=hidden name=sort value="created"> </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> <span dir="LTR">Search:</span> <b>keyword:new</b> <br> <div class=resultbar> <div class=resultline></div> <div> <div class=pagelinkbox> <div> <td>Displaying 1-10 of 427 results found. </div> <div class=pagelinks> <font size=-1>page 1 <a href="/search?q=keyword%3anew&start=10&sort=created">2</a> <a href="/search?q=keyword%3anew&start=20&sort=created">3</a> <a href="/search?q=keyword%3anew&start=30&sort=created">4</a> <a href="/search?q=keyword%3anew&start=40&sort=created">5</a> <a href="/search?q=keyword%3anew&start=50&sort=created">6</a> <a href="/search?q=keyword%3anew&start=60&sort=created">7</a> <a href="/search?q=keyword%3anew&start=70&sort=created">8</a> <a href="/search?q=keyword%3anew&start=80&sort=created">9</a> <a href="/search?q=keyword%3anew&start=90&sort=created">10</a> ... <a href="/search?q=keyword%3anew&start=420&sort=created">43</a> </font> </div> </div> </div> <div>      <font size=-1>Sort: <a href="/search?q=keyword%3anew">relevance</a> | <a href="/search?q=keyword%3anew&sort=references">references</a> | <a href="/search?q=keyword%3anew&sort=number">number</a> | <a href="/search?q=keyword%3anew&sort=modified">modified</a> | created </font>      <font size=-1>Format: long | <a href="/search?q=keyword%3anew&fmt=short&sort=created">short</a> | <a href="/search?q=keyword%3anew&fmt=data&sort=created">data</a> </font> </div> <div class=resultline></div> </div> <div class=space5></div> <div class=sequence> <div class=space1></div> <div class=line></div> <div class=seqhead> <div class=seqnumname> <div class=seqnum> <a href="/A381490">A381490</a> </div> <div class=seqname> Index of second half of decomposition of integers into pairs x(i)+y(j) based on <a href="/A380008" title="Numbers t whose binary expansion Sum 2^e_i has exponents e_i which are odious numbers (A000069).">A380008</a> and <a href="/A380009" title="Numbers t whose binary expansion Sum 2^e_i has exponents e_i which are evil numbers (A001969).">A380009</a>, respectively. </div> </div> <div class=scorerefs> +0<br> 0 </div> </div> <div> <div class=seqdatabox> <div class=seqdata>0, 1, 0, 1, 0, 1, 0, 1, 2, 3, 2, 3, 2, 3, 2, 3, 0, 1, 0, 1, 0, 1, 0, 1, 2, 3, 2, 3, 2, 3, 2, 3, 4, 5, 4, 5, 4, 5, 4, 5, 6, 7, 6, 7, 6, 7, 6, 7, 4, 5, 4, 5, 4, 5, 4, 5, 6, 7, 6, 7, 6, 7, 6, 7, 8, 9, 8, 9, 8, 9, 8, 9, 10, 11, 10, 11, 10, 11, 10, 11, 8, 9, 8, 9, 8, 9, 8, 9</div> <div class=seqdatalinks> (<a href="/A381490/list">list</a>; <a href="/A381490/graph">graph</a>; <a href="/search?q=A381490+-id:A381490">refs</a>; <a href="/A381490/listen">listen</a>; <a href="/history?seq=A381490">history</a>; <a href="/search?q=id:A381490&fmt=text">text</a>; <a href="/A381490/internal">internal format</a>) </div> </div> </div> <div class=entry> <div class=section> <div class=sectname>OFFSET</div> <div class=sectbody> <div class=sectline>0,9</div> </div> </div> <div class=section> <div class=sectname>COMMENTS</div> <div class=sectbody> <div class=sectline>One coordinate of a recursive non-self-intersecting walk on the square lattice Z^2.</div> <div class=sectline>Every integer appears infinitely many times in the sequence.</div> </div> </div> <div class=section> <div class=sectname>LINKS</div> <div class=sectbody> <div class=sectline><a href="/A381490/b381490.txt">Table of n, a(n) for n=0..87.</a></div> <div class=sectline>Luis Rato, <a href="/A380009/a380009.png">Plot of an NZ-order curve</a>, containing the integers from 0 to 255.</div> <div class=sectline><a href="/index/Con#coordinates_2D_curves">Index entries for sequences related to coordinates of 2D curves</a></div> </div> </div> <div class=section> <div class=sectname>FORMULA</div> <div class=sectbody> <div class=sectline>n = <a href="/A380008" title="Numbers t whose binary expansion Sum 2^e_i has exponents e_i which are odious numbers (A000069).">A380008</a>(<a href="/A381489" title="Index of first half of decomposition of integers into pairs x(i)+y(j) based on A380008 and A380009, respectively.">A381489</a>(n)) + <a href="/A380009" title="Numbers t whose binary expansion Sum 2^e_i has exponents e_i which are evil numbers (A001969).">A380009</a>(a(n))</div> </div> </div> <div class=section> <div class=sectname>EXAMPLE</div> <div class=sectbody> <div class=sectline><a href="/A380008" title="Numbers t whose binary expansion Sum 2^e_i has exponents e_i which are odious numbers (A000069).">A380008</a>( <a href="/A381489" title="Index of first half of decomposition of integers into pairs x(i)+y(j) based on A380008 and A380009, respectively.">A381489</a>(14)) + <a href="/A380009" title="Numbers t whose binary expansion Sum 2^e_i has exponents e_i which are evil numbers (A001969).">A380009</a>(a(14)) = <a href="/A380008" title="Numbers t whose binary expansion Sum 2^e_i has exponents e_i which are odious numbers (A000069).">A380008</a>(3) + <a href="/A380009" title="Numbers t whose binary expansion Sum 2^e_i has exponents e_i which are evil numbers (A001969).">A380009</a>(2) = 6+8 = 14</div> </div> </div> <div class=section> <div class=sectname>CROSSREFS</div> <div class=sectbody> <div class=sectline>Cf. <a href="/A381489" title="Index of first half of decomposition of integers into pairs x(i)+y(j) based on A380008 and A380009, respectively.">A381489</a></div> <div class=sectline>Cf. <a href="/A380008" title="Numbers t whose binary expansion Sum 2^e_i has exponents e_i which are odious numbers (A000069).">A380008</a> (indices of 0's), <a href="/A380009" title="Numbers t whose binary expansion Sum 2^e_i has exponents e_i which are evil numbers (A001969).">A380009</a>.</div> </div> </div> <div class=section> <div class=sectname>KEYWORD</div> <div class=sectbody> <div class=sectline><span title="it is very easy to produce terms of sequence">easy</span>,<span title="a sequence of nonnegative numbers">nonn</span>,<b><span title="added within the last two weeks">new</span></b></div> </div> </div> <div class=section> <div class=sectname>AUTHOR</div> <div class=sectbody> <div class=sectline><a href="/wiki/User:Luis_Rato">Luis Rato</a>, Feb 25 2025</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 class=sequence> <div class=space1></div> <div class=line></div> <div class=seqhead> <div class=seqnumname> <div class=seqnum> <a href="/A381489">A381489</a> </div> <div class=seqname> Index of first half of decomposition of integers into pairs x(i)+y(j) based on <a href="/A380008" title="Numbers t whose binary expansion Sum 2^e_i has exponents e_i which are odious numbers (A000069).">A380008</a> and <a href="/A380009" title="Numbers t whose binary expansion Sum 2^e_i has exponents e_i which are evil numbers (A001969).">A380009</a>, respectively. </div> </div> <div class=scorerefs> +0<br> 0 </div> </div> <div> <div class=seqdatabox> <div class=seqdata>0, 0, 1, 1, 2, 2, 3, 3, 0, 0, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 4, 4, 5, 5, 6, 6, 7, 7, 0, 0, 1, 1, 2, 2, 3, 3, 0, 0, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 4, 4, 5, 5, 6, 6, 7, 7, 0, 0, 1, 1, 2, 2, 3, 3, 0, 0, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 4, 4, 5, 5, 6, 6, 7, 7</div> <div class=seqdatalinks> (<a href="/A381489/list">list</a>; <a href="/A381489/graph">graph</a>; <a href="/search?q=A381489+-id:A381489">refs</a>; <a href="/A381489/listen">listen</a>; <a href="/history?seq=A381489">history</a>; <a href="/search?q=id:A381489&fmt=text">text</a>; <a href="/A381489/internal">internal format</a>) </div> </div> </div> <div class=entry> <div class=section> <div class=sectname>OFFSET</div> <div class=sectbody> <div class=sectline>0,5</div> </div> </div> <div class=section> <div class=sectname>COMMENTS</div> <div class=sectbody> <div class=sectline>One coordinate of a recursive non-self-intersecting walk on the square lattice Z^2.</div> <div class=sectline>Every integer appears infinitely many times in the sequence.</div> </div> </div> <div class=section> <div class=sectname>LINKS</div> <div class=sectbody> <div class=sectline><a href="/A381489/b381489.txt">Table of n, a(n) for n=0..95.</a></div> <div class=sectline>Luis Rato, <a href="/A380009/a380009.png">Plot of an NZ-order curve</a>, containing the integers from 0 to 255.</div> <div class=sectline><a href="/index/Con#coordinates_2D_curves">Index entries for sequences related to coordinates of 2D curves</a></div> </div> </div> <div class=section> <div class=sectname>FORMULA</div> <div class=sectbody> <div class=sectline>n = <a href="/A380008" title="Numbers t whose binary expansion Sum 2^e_i has exponents e_i which are odious numbers (A000069).">A380008</a>(a(n)) + <a href="/A380009" title="Numbers t whose binary expansion Sum 2^e_i has exponents e_i which are evil numbers (A001969).">A380009</a>(<a href="/A381490" title="Index of second half of decomposition of integers into pairs x(i)+y(j) based on A380008 and A380009, respectively.">A381490</a>(n)).</div> </div> </div> <div class=section> <div class=sectname>EXAMPLE</div> <div class=sectbody> <div class=sectline><a href="/A380008" title="Numbers t whose binary expansion Sum 2^e_i has exponents e_i which are odious numbers (A000069).">A380008</a>(a(14)) + <a href="/A380009" title="Numbers t whose binary expansion Sum 2^e_i has exponents e_i which are evil numbers (A001969).">A380009</a>(<a href="/A381490" title="Index of second half of decomposition of integers into pairs x(i)+y(j) based on A380008 and A380009, respectively.">A381490</a>(14)) = A3800008(3) + <a href="/A380009" title="Numbers t whose binary expansion Sum 2^e_i has exponents e_i which are evil numbers (A001969).">A380009</a>(2) = 6+8 = 14.</div> </div> </div> <div class=section> <div class=sectname>CROSSREFS</div> <div class=sectbody> <div class=sectline>Cf. <a href="/A380008" title="Numbers t whose binary expansion Sum 2^e_i has exponents e_i which are odious numbers (A000069).">A380008</a>, <a href="/A380009" title="Numbers t whose binary expansion Sum 2^e_i has exponents e_i which are evil numbers (A001969).">A380009</a>, <a href="/A381490" title="Index of second half of decomposition of integers into pairs x(i)+y(j) based on A380008 and A380009, respectively.">A381490</a>.</div> </div> </div> <div class=section> <div class=sectname>KEYWORD</div> <div class=sectbody> <div class=sectline><span title="it is very easy to produce terms of sequence">easy</span>,<span title="a sequence of nonnegative numbers">nonn</span>,<b><span title="added within the last two weeks">new</span></b></div> </div> </div> <div class=section> <div class=sectname>AUTHOR</div> <div class=sectbody> <div class=sectline><a href="/wiki/User:Luis_Rato">Luis Rato</a>, Feb 25 2025</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 class=sequence> <div class=space1></div> <div class=line></div> <div class=seqhead> <div class=seqnumname> <div class=seqnum> <a href="/A381294">A381294</a> </div> <div class=seqname> Smallest number k such that there are n sets A_1,...,A_n with each A_i being a subset of {1,...,k} and the intersection of A_i and A_j has size |i-j| for all 1 <= i < j <= n. </div> </div> <div class=scorerefs> +0<br> 0 </div> </div> <div> <div class=seqdatabox> <div class=seqdata>0, 0, 1, 2, 5, 9, 16, 24, 36, 50, 70, 91, 120, 150, 189, 231, 280, 336, 398, 468, 547, 630, 728</div> <div class=seqdatalinks> (<a href="/A381294/list">list</a>; <a href="/A381294/graph">graph</a>; <a href="/search?q=A381294+-id:A381294">refs</a>; <a href="/A381294/listen">listen</a>; <a href="/history?seq=A381294">history</a>; <a href="/search?q=id:A381294&fmt=text">text</a>; <a href="/A381294/internal">internal format</a>) </div> </div> </div> <div class=entry> <div class=section> <div class=sectname>OFFSET</div> <div class=sectbody> <div class=sectline>0,4</div> </div> </div> <div class=section> <div class=sectname>COMMENTS</div> <div class=sectbody> <div class=sectline>k is in Omega(n^3/2) and O(n^3).</div> </div> </div> <div class=section> <div class=sectname>LINKS</div> <div class=sectbody> <div class=sectline><a href="/A381294/b381294.txt">Table of n, a(n) for n=0..22.</a></div> <div class=sectline>Jonas Seiler, <a href="/A381294/a381294.txt">Optimal solution sets A_1,..,A_n for each n=0..22</a></div> <div class=sectline>Jonas Seiler, <a href="https://github.com/HerrPixel/A381294">Julia Code for calculating the sequence</a></div> <div class=sectline>Jonas Seiler, <a href="/A381294/a381294.pdf">Summary of results including upper and lower bounds</a></div> </div> </div> <div class=section> <div class=sectname>EXAMPLE</div> <div class=sectbody> <div class=sectline>For n = 4, k = 5 is optimal with the following solution:</div> <div class=sectline> A_1 = {1,2,3,4},</div> <div class=sectline> A_2 = {1,5},</div> <div class=sectline> A_3 = {1,2},</div> <div class=sectline> A_4 = {1,3,4,5}.</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="more terms are needed! please extend this sequence">more</span>,<b><span title="added within the last two weeks">new</span></b></div> </div> </div> <div class=section> <div class=sectname>AUTHOR</div> <div class=sectbody> <div class=sectline><a href="/wiki/User:Jonas_Seiler">Jonas Seiler</a>, Feb 19 2025</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 class=sequence> <div class=space1></div> <div class=line></div> <div class=seqhead> <div class=seqnumname> <div class=seqnum> <a href="/A380770">A380770</a> </div> <div class=seqname> Number of letters in the Slovene name of n (feminine, nominative), excluding spaces. </div> </div> <div class=scorerefs> +0<br> 0 </div> </div> <div> <div class=seqdatabox> <div class=seqdata>3, 3, 3, 3, 5, 3, 4, 5, 4, 5, 5, 6, 8, 8, 10, 8, 9, 10, 9, 10, 7, 12, 12, 12, 14, 12, 13, 14, 13, 14, 8, 13, 13, 13, 15, 13, 14, 15, 14, 15, 10, 15, 15, 15, 17, 15, 16, 17, 16, 17, 8, 13, 13, 13, 15, 13, 14, 15, 14, 15, 9, 14, 14, 14, 16, 14, 15, 16, 15, 16, 10, 15, 15, 15, 17, 15, 16, 17, 16, 17, 9, 14, 14, 14, 16, 14, 15, 16, 15</div> <div class=seqdatalinks> (<a href="/A380770/list">list</a>; <a href="/A380770/graph">graph</a>; <a href="/search?q=A380770+-id:A380770">refs</a>; <a href="/A380770/listen">listen</a>; <a href="/history?seq=A380770">history</a>; <a href="/search?q=id:A380770&fmt=text">text</a>; <a href="/A380770/internal">internal format</a>) </div> </div> </div> <div class=entry> <div class=section> <div class=sectname>OFFSET</div> <div class=sectbody> <div class=sectline>0,1</div> </div> </div> <div class=section> <div class=sectname>COMMENTS</div> <div class=sectbody> <div class=sectline>Repeatedly applying the map k -> a(k) to any starting value n always leads to 3 = "tri".</div> <div class=sectline>There is difference in gender (nominative) for number 1 and number 2.</div> <div class=sectline>1 - en (m.), ena (f.), eno (n.)</div> <div class=sectline>2 - dva (m.), dve (f.), dve (n.)</div> <div class=sectline>and similar 101, 201, etc, ...</div> <div class=sectline>All other numbers have the same form for all genders.</div> </div> </div> <div class=section> <div class=sectname>LINKS</div> <div class=sectbody> <div class=sectline><a href="/A380770/b380770.txt">Table of n, a(n) for n=0..88.</a></div> <div class=sectline>艩USS, <a href="http://www2.arnes.si/~lmarus/suss/arhiv/suss-arhiv-000396.html">How do you spell 143800 in words?</a> (in Slovenian).</div> <div class=sectline><a href="/index/Lc#letters">Index entries for sequences related to number of letters in n</a></div> </div> </div> <div class=section> <div class=sectname>EXAMPLE</div> <div class=sectbody> <div class=sectline>a(0)=3 [ni膷], a(1)=3 [ena], a(2)=3 [dve], a(3)=3 [tri], a(4)=5 [拧tiri]</div> </div> </div> <div class=section> <div class=sectname>PROG</div> <div class=sectbody> <div class=sectline>(Python)</div> <div class=sectline>from num2words import num2words</div> <div class=sectline>def a(n):</div> <div class=sectline> return len(num2words(n, lang='sl').replace(' ', ''))</div> <div class=sectline>print([a(n) for n in range(1000)])</div> </div> </div> <div class=section> <div class=sectname>CROSSREFS</div> <div class=sectbody> <div class=sectline>Cf. <a href="/A005589" title="Number of letters in the US English name of n, excluding spaces and hyphens.">A005589</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="depends on words in some language">word</span>,<b><span title="added within the last two weeks">new</span></b></div> </div> </div> <div class=section> <div class=sectname>AUTHOR</div> <div class=sectbody> <div class=sectline><a href="/wiki/User:Andrej_Jakobcic">Andrej Jakobcic</a>, Feb 02 2025</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 class=sequence> <div class=space1></div> <div class=line></div> <div class=seqhead> <div class=seqnumname> <div class=seqnum> <a href="/A381423">A381423</a> </div> <div class=seqname> Exponent of x of maximal coefficient in Hermite polynomial of order n. </div> </div> <div class=scorerefs> +0<br> 0 </div> </div> <div> <div class=seqdatabox> <div class=seqdata>0, 1, 2, 3, 4, 1, 2, 3, 4, 5, 2, 3, 4, 5, 6, 3, 4, 5, 6, 7, 4, 5, 6, 7, 4, 5, 6, 7, 8, 5, 6, 7, 8, 5, 6, 7, 8, 9, 6, 7, 8, 9, 6, 7, 8, 9, 10, 7, 8, 9, 10, 7, 8, 9, 10, 11, 8, 9, 10, 11, 8, 9, 10, 11, 12, 9, 10, 11, 12, 9, 10, 11, 12, 9, 10, 11, 12, 13, 10</div> <div class=seqdatalinks> (<a href="/A381423/list">list</a>; <a href="/A381423/graph">graph</a>; <a href="/search?q=A381423+-id:A381423">refs</a>; <a href="/A381423/listen">listen</a>; <a href="/history?seq=A381423">history</a>; <a href="/search?q=id:A381423&fmt=text">text</a>; <a href="/A381423/internal">internal format</a>) </div> </div> </div> <div class=entry> <div class=section> <div class=sectname>OFFSET</div> <div class=sectbody> <div class=sectline>0,3</div> </div> </div> <div class=section> <div class=sectname>COMMENTS</div> <div class=sectbody> <div class=sectline>The exponent is always unique. The coefficients, in absolute value, follow a unimodal pattern, and their signs alternate. If the maximum absolute coefficient appears twice due to symmetry (e.g., H_8(x)), the terms will have opposite signs, ensuring a unique exponent for the maximum signed coefficient.</div> <div class=sectline>Conjecture: Differences are either 1 or -3; more specifically the patterns (1,1,1,-3) or (1,1,1,1,-3), with position of those patterns appearing at linearly and quadratically spaced intervals, respectively. Seems to grow O(n^(1/2))</div> </div> </div> <div class=section> <div class=sectname>LINKS</div> <div class=sectbody> <div class=sectline><a href="/A381423/b381423.txt">Table of n, a(n) for n=0..78.</a></div> </div> </div> <div class=section> <div class=sectname>EXAMPLE</div> <div class=sectbody> <div class=sectline>For n = 5, H_5(x) = 32*x^5 - 160*x^3 + 120*x. The maximal coefficient is 120 (we take signs into account, so -160 < 120), occurring at x^1, hence a(5) = 1.</div> </div> </div> <div class=section> <div class=sectname>MATHEMATICA</div> <div class=sectbody> <div class=sectline>Table[(PositionLargest@CoefficientList[HermiteH[n, x], x])[[1]] - 1, {n, 0, 100}]</div> </div> </div> <div class=section> <div class=sectname>PROG</div> <div class=sectbody> <div class=sectline>(PARI) a(n) = my(p=polhermite(n), m=vecmax(Vec(p))); for(i=0, poldegree(p), if (polcoef(p, i) == m, return(i))); \\ <a href="/wiki/User:Michel_Marcus">Michel Marcus</a>, Feb 23 2025</div> </div> </div> <div class=section> <div class=sectname>CROSSREFS</div> <div class=sectbody> <div class=sectline>Cf. <a href="/A277280" title="Maximal coefficient in Hermite polynomial of order n.">A277280</a> (maximal coefficient).</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>,<b><span title="added within the last two weeks">new</span></b></div> </div> </div> <div class=section> <div class=sectname>AUTHOR</div> <div class=sectbody> <div class=sectline><a href="/wiki/User:Mike_Sheppard">Mike Sheppard</a>, Feb 23 2025</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 class=sequence> <div class=space1></div> <div class=line></div> <div class=seqhead> <div class=seqnumname> <div class=seqnum> <a href="/A380596">A380596</a> </div> <div class=seqname> Numbers with embedded palindromes as proper substrings of the term. </div> </div> <div class=scorerefs> +0<br> 0 </div> </div> <div> <div class=seqdatabox> <div class=seqdata>100, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 122, 133, 144, 155, 166, 177, 188, 199, 200, 211, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 233, 244, 255, 266, 277, 288, 299, 300, 311, 322, 330, 331, 332, 333, 334, 335, 336, 337, 338, 339, 344, 355, 366, 377, 388, 399</div> <div class=seqdatalinks> (<a href="/A380596/list">list</a>; <a href="/A380596/graph">graph</a>; <a href="/search?q=A380596+-id:A380596">refs</a>; <a href="/A380596/listen">listen</a>; <a href="/history?seq=A380596">history</a>; <a href="/search?q=id:A380596&fmt=text">text</a>; <a href="/A380596/internal">internal format</a>) </div> </div> </div> <div class=entry> <div class=section> <div class=sectname>OFFSET</div> <div class=sectbody> <div class=sectline>1,1</div> </div> </div> <div class=section> <div class=sectname>COMMENTS</div> <div class=sectbody> <div class=sectline>An embedded palindrome is a substring of at least two contiguous digits (since a single digit is trivially a palindrome). E.g., 121 is a palindrome, but has no embedded palindromes; 110 has the embedded palindrome "11".</div> <div class=sectline>Alternatively, k contains a proper substring of the form dd or ded, where d and e are single decimal digits (i.e., a length-2 or -3 palindrome). - <a href="/wiki/User:Michael_S._Branicky">Michael S. Branicky</a>, Feb 08 2025</div> </div> </div> <div class=section> <div class=sectname>LINKS</div> <div class=sectbody> <div class=sectline><a href="/A380596/b380596.txt">Table of n, a(n) for n=1..57.</a></div> </div> </div> <div class=section> <div class=sectname>EXAMPLE</div> <div class=sectbody> <div class=sectline>100 is a term, since "00" is a palindrome; 1001 is a term for the same reason.</div> <div class=sectline>1020 is a term, since "020" is a palindrome; 10201 is a term for the same reason.</div> </div> </div> <div class=section> <div class=sectname>PROG</div> <div class=sectbody> <div class=sectline>(Python)</div> <div class=sectline>from itertools import combinations</div> <div class=sectline>def get_all_substrings(string):</div> <div class=sectline> length = len(string) + 1</div> <div class=sectline> return [string[x:y] for x, y in combinations(range(length), r=2)]</div> <div class=sectline>def is_palindrome(n):</div> <div class=sectline> return str(n) == str(n)[::-1]</div> <div class=sectline>def ok(n):</div> <div class=sectline> subsets = get_all_substrings(str(n))</div> <div class=sectline> subsets = [subset for subset in subsets if is_palindrome(subset) and len(subset)>1 and len(subset)<len(str(n))]</div> <div class=sectline> return len(subsets)>0</div> <div class=sectline>print([k for k in range (100, 400) if ok(k)])</div> <div class=sectline>(Python)</div> <div class=sectline>def ok(n):</div> <div class=sectline> s = str(n)</div> <div class=sectline> return any(p == p[::-1] and len(p) < len(s) for p in (s[i:i+j] for j in (2, 3) for i in range(len(s)-j+1)))</div> <div class=sectline>print([k for k in range(400) if ok(k)]) # <a href="/wiki/User:Michael_S._Branicky">Michael S. Branicky</a>, Feb 08 2025</div> </div> </div> <div class=section> <div class=sectname>CROSSREFS</div> <div class=sectbody> <div class=sectline>Cf. <a href="/A002113" title="Palindromes in base 10.">A002113</a>.</div> <div class=sectline>Significant overlap with <a href="/A044821" title="Positive integers having distinct base-10 run lengths.">A044821</a> for terms below 1000.</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>,<b><span title="added within the last two weeks">new</span></b></div> </div> </div> <div class=section> <div class=sectname>AUTHOR</div> <div class=sectbody> <div class=sectline><a href="/wiki/User:James_S._DeArmon">James S. DeArmon</a>, Jan 27 2025</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 class=sequence> <div class=space1></div> <div class=line></div> <div class=seqhead> <div class=seqnumname> <div class=seqnum> <a href="/A379883">A379883</a> </div> <div class=seqname> a(1) = 1. Let j = a(n-1) and r = <a href="/A046144" title="Number of primitive roots modulo n.">A046144</a>(j). Then for n > 1, if j is novel and r > 0, a(n) = r. If j is novel and r = 0 then a(n) = 1. If j has occurred k (>1) times already then a(n) = k*j. </div> </div> <div class=scorerefs> +0<br> 0 </div> </div> <div> <div class=seqdatabox> <div class=seqdata>1, 1, 2, 1, 3, 1, 4, 1, 5, 2, 4, 8, 1, 6, 1, 7, 2, 6, 12, 1, 8, 16, 1, 9, 2, 8, 24, 1, 10, 2, 10, 20, 1, 11, 4, 12, 24, 48, 1, 12, 36, 1, 13, 4, 16, 32, 1, 14, 2, 12, 48, 96, 1, 15, 1, 16, 48, 144, 1, 17, 8, 32, 64, 1, 18, 2, 14, 28, 1, 19, 6, 18, 36, 72, 1, 20, 40, 1, 21, 22, 4, 20, 60, 1, 23, 10, 30, 1, 24, 72, 144, 288, 1, 25, 8, 40, 80, 1, 26, 4</div> <div class=seqdatalinks> (<a href="/A379883/list">list</a>; <a href="/A379883/graph">graph</a>; <a href="/search?q=A379883+-id:A379883">refs</a>; <a href="/A379883/listen">listen</a>; <a href="/history?seq=A379883">history</a>; <a href="/search?q=id:A379883&fmt=text">text</a>; <a href="/A379883/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>In other words if j = a(n-1) has not occurred earlier and has r (> 0) primitive roots then a(n) = r. Cases where novel <a href="/A046144" title="Number of primitive roots modulo n.">A046144</a>(j) = 0 cannot be counted multiplicatively (as k*j) for repeats, so a(n) = 1 is designed to permit the sequence to continue past such points, which means including in the count of 1's terms following (1,2,3,4,6), for which it is true that r = 1. Terms beyond a(12) = 8 which count the number of 1's (by the second condition) give the cardinality of terms with no primitive roots, plus the few (5) cases of terms with primitive root = 1.</div> <div class=sectline>Every even number m in <a href="/A380594" title="a(n) is the number of positive integers having 2n primitive roots.">A380594</a> appears finitely many times, consequent to occasions of integers v (>6) for which <a href="/A046144" title="Number of primitive roots modulo n.">A046144</a>(v) = m, and to repetitions (k*j) = m for j even. However every odd number appears once only (consequent to odd counts of 1's). The odd numbers appear in order, and since 2 precedes all of them, the primes are in order.</div> </div> </div> <div class=section> <div class=sectname>LINKS</div> <div class=sectbody> <div class=sectline>Michael De Vlieger, <a href="/A379883/b379883.txt">Table of n, a(n) for n = 1..10000</a></div> <div class=sectline>Michael De Vlieger, <a href="/A379883/a379883.png">Log log scatterplot of a(n)</a>, n = 1..2^20.</div> </div> </div> <div class=section> <div class=sectname>EXAMPLE</div> <div class=sectbody> <div class=sectline>a(2) = 1 since a(1)=1 and and 1 has one primitive root. Since 1 has been seen twice, a(3) = 2 and then a(4) = 1 since 2 is a novel term with one primitive root.</div> <div class=sectline>a(9) = 5, a novel term with two primitive roots so a(10) = 2, which has appeared once before (a(3)=2), so a(11) = 4, the second occurrence of 4 so a(12) = 8, a novel term with no primitive roots, meaning that a(13) = 1. The count of 1's is now 6, so a(14) = 6, meaning 5 prior terms with one primitive root and one with none.</div> </div> </div> <div class=section> <div class=sectname>MATHEMATICA</div> <div class=sectbody> <div class=sectline>nn = 120; c[_] := 0; j = 1;</div> <div class=sectline>f[x_] := f[x] = Which[</div> <div class=sectline> x == 1, 1,</div> <div class=sectline> IntegerQ[PrimitiveRoot[x]], Nest[EulerPhi, x, 2],</div> <div class=sectline> True, 0];</div> <div class=sectline>{j}~Join~Reap[Monitor[Do[</div> <div class=sectline> If[c[j] == 0,</div> <div class=sectline> Set[k, # + Boole[# == 0]] &[f[j]]; c[j]++,</div> <div class=sectline> k = ++c[j]*j ];</div> <div class=sectline>j = Sow[k], {n, 2, nn}], n] ][[-1, 1]] (* <a href="/wiki/User:Michael_De_Vlieger">Michael De Vlieger</a>, Jan 09 2025 *)</div> </div> </div> <div class=section> <div class=sectname>CROSSREFS</div> <div class=sectbody> <div class=sectline>Cf. <a href="/A046144" title="Number of primitive roots modulo n.">A046144</a>, <a href="/A378508" title="Values taken by phi(phi(m)) (A010554).">A378508</a>, <a href="/A380594" title="a(n) is the number of positive integers having 2n primitive roots.">A380594</a>, <a href="/A380604" title="Numbers k such that there is no number i such that A046144(i) = 2*k.">A380604</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="it is very easy to produce terms of sequence">easy</span>,<b><span title="added within the last two weeks">new</span></b></div> </div> </div> <div class=section> <div class=sectname>AUTHOR</div> <div class=sectbody> <div class=sectline><a href="/wiki/User:David_James_Sycamore">David James Sycamore</a>, Jan 09 2025</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 class=sequence> <div class=space1></div> <div class=line></div> <div class=seqhead> <div class=seqnumname> <div class=seqnum> <a href="/A381697">A381697</a> </div> <div class=seqname> Zeroless integers of the form 10*k+1 such that the 9 integers 10*k+1..10*k+9 all belong to <a href="/A381631" title="allocated for Jakub Buczak">A381631</a>. </div> </div> <div class=scorerefs> +0<br> 0 </div> </div> <div> <div class=seqdatabox> <div class=seqdata>1, 1587474651, 1865775531, 2223331131, 2735465781, 2758657521, 2955787311, 3437557341, 3558772551, 3575611851, 3825477561, 4339513471, 5216934211, 5228577831, 5773583721, 7358739151, 7547751831, 7733285751, 9553837341, 11745456771, 11765169751, 12646455871</div> <div class=seqdatalinks> (<a href="/A381697/list">list</a>; <a href="/A381697/graph">graph</a>; <a href="/search?q=A381697+-id:A381697">refs</a>; <a href="/A381697/listen">listen</a>; <a href="/history?seq=A381697">history</a>; <a href="/search?q=id:A381697&fmt=text">text</a>; <a href="/A381697/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="/A381697/b381697.txt">Table of n, a(n) for n=1..22.</a></div> </div> </div> <div class=section> <div class=sectname>PROG</div> <div class=sectbody> <div class=sectline>(PARI) isOne(k) = my(d=digits(k)); ((k*vecprod(d)) % vecsum(d)) == 0; \\ <a href="/A381631" title="allocated for Jakub Buczak">A381631</a></div> <div class=sectline>chk(nn) = for (i=0, nn, my(x=10*i+1, d=digits(x)); if (vecmin(d), my(ok=1); for (j=0, 8, if (!isOne(x+j), ok=0; break); ); if (ok, print1(x, ", ")); ); );</div> </div> </div> <div class=section> <div class=sectname>CROSSREFS</div> <div class=sectbody> <div class=sectline>Cf. <a href="/A052382" title="Numbers without 0 as a digit, a.k.a. zeroless numbers.">A052382</a> (zeroless integers), <a href="/A381631" title="allocated for Jakub Buczak">A381631</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>,<b><span title="added within the last two weeks">new</span></b></div> </div> </div> <div class=section> <div class=sectname>AUTHOR</div> <div class=sectbody> <div class=sectline><a href="/wiki/User:Michel_Marcus">Michel Marcus</a>, Mar 04 2025</div> </div> </div> <div class=section> <div class=sectname>EXTENSIONS</div> <div class=sectbody> <div class=sectline>a(20)-a(22) from <a href="/wiki/User:Jinyuan_Wang">Jinyuan Wang</a>, Mar 05 2025</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 class=sequence> <div class=space1></div> <div class=line></div> <div class=seqhead> <div class=seqnumname> <div class=seqnum> <a href="/A381720">A381720</a> </div> <div class=seqname> Integers whose Hamming weight is a cube. </div> </div> <div class=scorerefs> +0<br> 0 </div> </div> <div> <div class=seqdatabox> <div class=seqdata>0, 1, 2, 4, 8, 16, 32, 64, 128, 255, 256, 383, 447, 479, 495, 503, 507, 509, 510, 512, 639, 703, 735, 751, 759, 763, 765, 766, 831, 863, 879, 887, 891, 893, 894, 927, 943, 951, 955, 957, 958, 975, 983, 987, 989, 990, 999, 1003, 1005, 1006, 1011, 1013, 1014</div> <div class=seqdatalinks> (<a href="/A381720/list">list</a>; <a href="/A381720/graph">graph</a>; <a href="/search?q=A381720+-id:A381720">refs</a>; <a href="/A381720/listen">listen</a>; <a href="/history?seq=A381720">history</a>; <a href="/search?q=id:A381720&fmt=text">text</a>; <a href="/A381720/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>The plot of terms of the form k - 2^floor(log_2(k)) shows quasi-periodic structures on the intervals [2^i, 2^(i+1)]. In general, all sequences of the form "Integers whose Hamming weight is f(x)", where f(x) is an integer valued function, are quasi-periodic on intervals [2^i, 2^(i+1)].</div> <div class=sectline>The powers of 2 (<a href="/A000079" title="Powers of 2: a(n) = 2^n.">A000079</a>) are terms.</div> <div class=sectline><a href="/A023690" title="Numbers with exactly 8 ones in binary expansion.">A023690</a> is a subsequence.</div> </div> </div> <div class=section> <div class=sectname>LINKS</div> <div class=sectbody> <div class=sectline><a href="/A381720/b381720.txt">Table of n, a(n) for n=1..53.</a></div> </div> </div> <div class=section> <div class=sectname>EXAMPLE</div> <div class=sectbody> <div class=sectline>For k = 255: <a href="/A000120" title="1's-counting sequence: number of 1's in binary expansion of n (or the binary weight of n).">A000120</a>(255) = 8 = 2^3 is a cube, thus 255 is a term.</div> </div> </div> <div class=section> <div class=sectname>MATHEMATICA</div> <div class=sectbody> <div class=sectline>Select[Range[0, 1200], IntegerQ[Surd[DigitCount[#, 2, 1], 3]] &] (* <a href="/wiki/User:Amiram_Eldar">Amiram Eldar</a>, Mar 05 2025 *)</div> </div> </div> <div class=section> <div class=sectname>PROG</div> <div class=sectbody> <div class=sectline>(PARI) isok(k) = ispower(hammingweight(k), 3); \\ <a href="/wiki/User:Michel_Marcus">Michel Marcus</a>, Mar 05 2025</div> <div class=sectline>(Python)</div> <div class=sectline>from itertools import count, islice, combinations</div> <div class=sectline>from sympy import integer_nthroot</div> <div class=sectline>def <a href="/A381720" title="Integers whose Hamming weight is a cube.">A381720</a>_gen(): # generator of terms</div> <div class=sectline> a = []</div> <div class=sectline> yield 0</div> <div class=sectline> for l in count(1):</div> <div class=sectline> b = 1<<l-1</div> <div class=sectline> yield from sorted(sum(p)+b for i in range(1, integer_nthroot(l, 3)[0]+1) for p in combinations(a, i**3-1))</div> <div class=sectline> a.append(b)</div> <div class=sectline><a href="/A381720" title="Integers whose Hamming weight is a cube.">A381720</a>_list = list(islice(<a href="/A381720" title="Integers whose Hamming weight is a cube.">A381720</a>_gen(), 53)) # <a href="/wiki/User:Chai_Wah_Wu">Chai Wah Wu</a>, Mar 06 2025</div> </div> </div> <div class=section> <div class=sectname>CROSSREFS</div> <div class=sectbody> <div class=sectline>Cf. <a href="/A000079" title="Powers of 2: a(n) = 2^n.">A000079</a>, <a href="/A000120" title="1's-counting sequence: number of 1's in binary expansion of n (or the binary weight of n).">A000120</a>, <a href="/A000578" title="The cubes: a(n) = n^3.">A000578</a>, <a href="/A023690" title="Numbers with exactly 8 ones in binary expansion.">A023690</a>.</div> <div class=sectline>Cf. <a href="/A084561" title="Numbers with a square number of 1's in their binary expansion.">A084561</a>, <a href="/A344602" title="Integers whose Hamming weight is triangular.">A344602</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>,<b><span title="added within the last two weeks">new</span></b></div> </div> </div> <div class=section> <div class=sectname>AUTHOR</div> <div class=sectbody> <div class=sectline><a href="/wiki/User:Ctibor_O._Zizka">Ctibor O. Zizka</a>, Mar 05 2025</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 class=sequence> <div class=space1></div> <div class=line></div> <div class=seqhead> <div class=seqnumname> <div class=seqnum> <a href="/A381704">A381704</a> </div> <div class=seqname> Fibonacci numbers having a Fibonacci number of 1's in their binary representation. </div> </div> <div class=scorerefs> +0<br> 0 </div> </div> <div> <div class=seqdatabox> <div class=seqdata>1, 2, 3, 5, 8, 13, 21, 34, 55, 144, 233, 987, 4181, 6765, 17711, 832040, 3524578, 1836311903, 2971215073, 225851433717, 259695496911122585, 3928413764606871165730, 26925748508234281076009, 9969216677189303386214405760200, 638817435613190341905763972389505493</div> <div class=seqdatalinks> (<a href="/A381704/list">list</a>; <a href="/A381704/graph">graph</a>; <a href="/search?q=A381704+-id:A381704">refs</a>; <a href="/A381704/listen">listen</a>; <a href="/history?seq=A381704">history</a>; <a href="/search?q=id:A381704&fmt=text">text</a>; <a href="/A381704/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="/A381704/b381704.txt">Table of n, a(n) for n=1..25.</a></div> </div> </div> <div class=section> <div class=sectname>EXAMPLE</div> <div class=sectbody> <div class=sectline>F(10) = (55)_10 = (110111)_2 has five 1's in binary, 5 is a Fibonacci number, thus 55 is a term.</div> <div class=sectline>F(12) = (144)_10 = (10010000)_2 has two 1's in binary, 2 is a Fibonacci number, thus 144 is a term.</div> </div> </div> <div class=section> <div class=sectname>MATHEMATICA</div> <div class=sectbody> <div class=sectline>With[{f = Fibonacci[Range[2, 200]]}, Select[f, MemberQ[f, DigitCount[#, 2, 1] ] &]] (* <a href="/wiki/User:Amiram_Eldar">Amiram Eldar</a>, Mar 04 2025 *)</div> </div> </div> <div class=section> <div class=sectname>PROG</div> <div class=sectbody> <div class=sectline>(PARI) isfib(n) = my(k=n^2); k+=(k+1)<<2; issquare(k) || (n>0 && issquare(k-8)); \\ <a href="/A010056" title="Characteristic function of Fibonacci numbers: a(n) = 1 if n is a Fibonacci number, otherwise 0.">A010056</a></div> <div class=sectline>lista(nn) = for (n=2, nn, my(f = fibonacci(n)); if (isfib(hammingweight(f)), print1(f, ", ")); ); \\ <a href="/wiki/User:Michel_Marcus">Michel Marcus</a>, Mar 04 2025</div> </div> </div> <div class=section> <div class=sectname>CROSSREFS</div> <div class=sectbody> <div class=sectline>Cf. <a href="/A000045" title="Fibonacci numbers: F(n) = F(n-1) + F(n-2) with F(0) = 0 and F(1) = 1.">A000045</a>, <a href="/A004685" title="Fibonacci numbers written in base 2.">A004685</a>, <a href="/A010056" title="Characteristic function of Fibonacci numbers: a(n) = 1 if n is a Fibonacci number, otherwise 0.">A010056</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>,<b><span title="added within the last two weeks">new</span></b></div> </div> </div> <div class=section> <div class=sectname>AUTHOR</div> <div class=sectbody> <div class=sectline><a href="/wiki/User:Ctibor_O._Zizka">Ctibor O. Zizka</a>, Mar 04 2025</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 class=resultbar> <div class=resultline></div> <div> <div class=pagelinkbox> <div></div> <div class=pagelinks> <font size=-1>page 1 <a href="/search?q=keyword%3anew&start=10&sort=created">2</a> <a href="/search?q=keyword%3anew&start=20&sort=created">3</a> <a href="/search?q=keyword%3anew&start=30&sort=created">4</a> <a href="/search?q=keyword%3anew&start=40&sort=created">5</a> <a href="/search?q=keyword%3anew&start=50&sort=created">6</a> <a href="/search?q=keyword%3anew&start=60&sort=created">7</a> <a href="/search?q=keyword%3anew&start=70&sort=created">8</a> <a href="/search?q=keyword%3anew&start=80&sort=created">9</a> <a href="/search?q=keyword%3anew&start=90&sort=created">10</a> ... <a href="/search?q=keyword%3anew&start=420&sort=created">43</a> </font> </div> </div> </div> <div class=resultline></div> </div> <center><p><font size=-1> Search completed in 0.121 seconds </font></p></center> </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 March 6 21:02 EST 2025. 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