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A259396 - 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>A259396 - OEIS</title> <link rel="search" type="application/opensearchdescription+xml" title="OEIS" href="/oeis.xml"> <script> var myURL = "\/A259396" 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=%2fA259396">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="A259396 - 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> A259396 </div> <div class=seqname> Length of runs of identical terms in <a href="/A080378" title="Residues mod 4 of the n-th difference between consecutive primes.">A080378</a>. </div> </div> <div class=scorerefs> 0 </div> </div> <div> <div class=seqdatabox> <div class=seqdata>1, 2, 1, 1, 1, 1, 1, 3, 1, 1, 1, 4, 1, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 6, 1, 5, 1, 1, 3, 1, 1, 8, 1, 3, 1, 1, 1, 4, 1, 1, 1, 2, 1, 1, 3, 5, 1, 1, 2, 1, 6, 1, 1, 14, 1, 1, 1, 2, 1, 3, 2, 1, 1, 1, 1, 1, 1, 2, 2, 1, 3, 2, 1, 3, 1, 3, 1, 1, 1, 1, 1, 1, 4, 1, 2, 3, 1, 2, 1, 1, 2, 11, 1, 1, 1, 2, 1, 5</div> <div class=seqdatalinks> (<a href="/A259396/list">list</a>; <a href="/A259396/graph">graph</a>; <a href="/search?q=A259396+-id:A259396">refs</a>; <a href="/A259396/listen">listen</a>; <a href="/history?seq=A259396">history</a>; <a href="/search?q=id:A259396&fmt=text">text</a>; <a href="/A259396/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="/A259396/b259396.txt">Table of n, a(n) for n=1..98.</a></div> </div> </div> <div class=section> <div class=sectname>MATHEMATICA</div> <div class=sectbody> <div class=sectline>Length/@Split[Mod[Differences[Prime[Range[200]]], 4]]</div> </div> </div> <div class=section> <div class=sectname>CROSSREFS</div> <div class=sectbody> <div class=sectline>Cf. <a href="/A001223" title="Prime gaps: differences between consecutive primes.">A001223</a>, <a href="/A080378" title="Residues mod 4 of the n-th difference between consecutive primes.">A080378</a>, <a href="/A259360" title="Initial prime in the least set of exactly n+1 consecutive primes with n gaps all multiples of 4.">A259360</a>.</div> <div class=sectline>Sequence in context: <a href="/A220122" title="Number A(n,k) of tilings of a k X n rectangle using integer-sided rectangular tiles of area k; square array A(n,k), n>=0, k>...">A220122</a> <a href="/A101446" title="a(n)= least k such that n^k*(n^k-1)-1 is prime with n > 1.">A101446</a> <a href="/A333769" title="Irregular triangle read by rows where row k is the sequence of run-lengths of the k-th composition in standard order.">A333769</a> * <a href="/A328672" title="Number of integer partitions of n with relatively prime parts in which no two distinct parts are relatively prime.">A328672</a> <a href="/A368465" title="Number of even terms in each row of the iterates of the Christmas tree pattern map (A367508).">A368465</a> <a href="/A378222" title="Number of ordered factorizations of the odd part of n into factors > 1.">A378222</a></div> <div class=sectline>Adjacent sequences: <a href="/A259393" title="Expansion of f(-x^3, -x^7) * f(x^4, x^6) / psi(-x)^2 in powers of x where psi(), f(,) are Ramanujan theta functions.">A259393</a> <a href="/A259394" title="Primes of the form (sum of the digits of k to consecutive powers starting at 1) + k, ordered by k (duplicates allowed).">A259394</a> <a href="/A259395" title="a(n) = -3*n^2*(n-1)^4*(n+1)*(11*n^3+49*n^2-439*n+171).">A259395</a> * <a href="/A259397" title="Numbers n with the property that it is possible to write the base 2 expansion of n as concat(a_2,b_2), with a_2>0 and b_2>0 ...">A259397</a> <a href="/A259398" title="Numbers n such that numerator(sigma(n)/n) = reverse(denominator(sigma(n)/n)).">A259398</a> <a href="/A259399" title="a(n) = Sum_{k=0..n} p(k)^2, where p(k) is the partition function A000041.">A259399</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:Zak_Seidov">Zak Seidov</a>, Jun 26 2015</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 November 24 19:22 EST 2024. Contains 378083 sequences.</div> <div class=legal> <a href="/wiki/Legal_Documents">License Agreements, Terms of Use, Privacy Policy</a> </div> </div> </center> </div> </body> </html>