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A181098 - 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>A181098 - OEIS</title> <link rel="search" type="application/opensearchdescription+xml" title="OEIS" href="/oeis.xml"> <script> var myURL = "\/A181098" 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=%2fA181098">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="A181098 - 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> A181098 </div> <div class=seqname> Primefree centuries (i.e., numbers k such that no prime exists between 100*k and 100*k+99). </div> </div> <div class=scorerefs> 27 </div> </div> <div> <div class=seqdatabox> <div class=seqdata>16718, 26378, 31173, 39336, 46406, 46524, 51782, 55187, 58374, 58452, 60129, 60850, 63338, 63762, 67898, 69587, 71299, 75652, 78035, 78269, 80277, 83674, 84213, 89052, 95490, 97080, 100881, 101527, 103438, 105916, 111772, 112967</div> <div class=seqdatalinks> (<a href="/A181098/list">list</a>; <a href="/A181098/graph">graph</a>; <a href="/search?q=A181098+-id:A181098">refs</a>; <a href="/A181098/listen">listen</a>; <a href="/history?seq=A181098">history</a>; <a href="/search?q=id:A181098&fmt=text">text</a>; <a href="/A181098/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>The first consecutive terms are 473267, 473268; see <a href="/A190639" title="Centuries whose prime pattern repeats in the next century.">A190639</a>. - <a href="/wiki/User:M._F._Hasler">M. F. Hasler</a>, May 15 2011</div> </div> </div> <div class=section> <div class=sectname>LINKS</div> <div class=sectbody> <div class=sectline>T. D. Noe, <a href="/A181098/b181098.txt">Table of n, a(n) for n = 1..1000</a></div> </div> </div> <div class=section> <div class=sectname>FORMULA</div> <div class=sectbody> <div class=sectline>a(n) = n + 100n/log n - O(n/log^2 n). - <a href="/wiki/User:Charles_R_Greathouse_IV">Charles R Greathouse IV</a>, Sep 08 2017</div> </div> </div> <div class=section> <div class=sectname>EXAMPLE</div> <div class=sectbody> <div class=sectline>16718 is a term because there is no prime between 1671800 and 1671899.</div> </div> </div> <div class=section> <div class=sectname>MATHEMATICA</div> <div class=sectbody> <div class=sectline>Flatten[Position[Differences[PrimePi[100*Range[0, 113000]]], 0]]-1 (* <a href="/wiki/User:Harvey_P._Dale">Harvey P. Dale</a>, Dec 18 2021 *)</div> </div> </div> <div class=section> <div class=sectname>PROG</div> <div class=sectbody> <div class=sectline>(PARI) is(n)=nextprime(100*n)>100*n+99 \\ <a href="/wiki/User:Charles_R_Greathouse_IV">Charles R Greathouse IV</a>, Apr 28 2015</div> </div> </div> <div class=section> <div class=sectname>CROSSREFS</div> <div class=sectbody> <div class=sectline>Cf. <a href="/A038822" title="Number of primes between 100n and 100n+99.">A038822</a> (number of primes between 100n and 100n+99), <a href="/A186311" title="Least k such that the interval 100k to 100k+99 has exactly n primes.">A186311</a> (first occurrences).</div> <div class=sectline>Cf. <a href="/A186393" title="Numbers k such that there is 1 prime between 100*k and 100*k + 99.">A186393</a>-<a href="/A186408" title="Numbers k such that there are 16 primes between 100*k and 100*k + 99.">A186408</a> (1 to 16 primes), <a href="/A186509" title="Numbers k such that there are 17 primes between 100*k and 100*k + 99.">A186509</a> (17 primes), <a href="/A361723" title="Numbers k such that there are 18 primes between 100*k and 100*k + 99.">A361723</a> (18 primes).</div> <div class=sectline>Sequence in context: <a href="/A345829" title="Numbers that are the sum of seven fourth powers in exactly seven ways.">A345829</a> <a href="/A224572" title="Number of (n+5) X 8 0..1 matrices with each 6 X 6 subblock idempotent.">A224572</a> <a href="/A186311" title="Least k such that the interval 100k to 100k+99 has exactly n primes.">A186311</a> * <a href="/A365813" title="Numbers which form a prime by appending a 3-digit number and form no primes by appending 1 digit or 2 digits.">A365813</a> <a href="/A202896" title="Number of (n+2)X8 binary arrays avoiding patterns 001 and 010 in rows, columns and nw-to-se diagonals.">A202896</a> <a href="/A183727" title="1/12 the number of (n+1) X 8 0..5 arrays with every 2 X 2 subblock strictly increasing clockwise or counterclockwise with on...">A183727</a></div> <div class=sectline>Adjacent sequences: <a href="/A181095" title="Permutation of positive integers created from sequence A008578(n) = noncomposites.">A181095</a> <a href="/A181096" title="Permutation of positive integers created from sequence A018252(n) = nonprimes.">A181096</a> <a href="/A181097" title="Permutation of positive integers created from sequence A002808(n) = composites.">A181097</a> * <a href="/A181099" title="Exchange rightmost two ternary digits of n > 1; a(0)=0, a(1)=3.">A181099</a> <a href="/A181100" title="Numbers k such that A028260(k) + 1 is prime.">A181100</a> <a href="/A181101" title="Triangle T(n,k) read by rows. T(1,1)=-1, n>1: If n/k=A020639(n) then 1 else 0.">A181101</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:Jeff_Burch">Jeff Burch</a>, Oct 02 2010</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 25 00:49 EST 2024. Contains 378089 sequences.</div> <div class=legal> <a href="/wiki/Legal_Documents">License Agreements, Terms of Use, Privacy Policy</a> </div> </div> </center> </div> </body> </html>