CINXE.COM
A190639 - 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>A190639 - OEIS</title> <link rel="search" type="application/opensearchdescription+xml" title="OEIS" href="/oeis.xml"> <script> var myURL = "\/A190639" 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=%2fA190639">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="A190639 - 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> A190639 </div> <div class=seqname> Centuries whose prime pattern repeats in the next century. </div> </div> <div class=scorerefs> 11 </div> </div> <div> <div class=seqdatabox> <div class=seqdata>473267, 726760, 1773439, 1808828, 1919128, 2131583, 2165420, 2339971, 2390652, 2518488, 2802591, 2844914, 2982584, 2996184, 3183263, 3193175, 3250986, 3418185, 3428241, 3633472, 3909324, 3953449, 4280455, 4303819, 4373399, 4658285, 4728653, 4978360, 5165402, 5254365</div> <div class=seqdatalinks> (<a href="/A190639/list">list</a>; <a href="/A190639/graph">graph</a>; <a href="/search?q=A190639+-id:A190639">refs</a>; <a href="/A190639/listen">listen</a>; <a href="/history?seq=A190639">history</a>; <a href="/search?q=id:A190639&fmt=text">text</a>; <a href="/A190639/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>Alternate definition: Numbers x such that for all N in [100x,100x+99], N is prime iff N+100 is prime.</div> <div class=sectline>Contains in particular the first of two consecutive prime-free centuries, i.e., N such that there is no prime in [100 N,100 (N+2)], cf. <a href="/A181098" title="Primefree centuries (i.e., numbers k such that no prime exists between 100*k and 100*k+99).">A181098</a>.</div> <div class=sectline>x belongs to this sequence if and only if the primality character of (100 * x) + k is the same as (100 * (x+1)) + k for all k = 0..99. - <a href="/wiki/User:V._Raman">V. Raman</a>, Dec 09 2012</div> </div> </div> <div class=section> <div class=sectname>LINKS</div> <div class=sectbody> <div class=sectline>Donovan Johnson, <a href="/A190639/b190639.txt">Table of n, a(n) for n = 1..1000</a></div> <div class=sectline>J. K. Andersen, in reply to R. Wood, <a href="http://groups.yahoo.com/group/primenumbers/message/22717">Re: First repetition of prime pattern within "centuries"</a>, Yahoo group "primenumbers", May 15, 2011.</div> <div class=sectline>Jens Kruse Andersen, Phil Carmody, Maximilian Hasler, <a href="/A190639/a190639.txt">First repetition of prime pattern within "centuries"</a>, digest of 11 messages in primenumbers Yahoo group, May 15, 2011.</div> </div> </div> <div class=section> <div class=sectname>FORMULA</div> <div class=sectbody> <div class=sectline>a(n) ~ n. In particular there are x - 200x/log x + O(x/log^2 x) members of this sequence below x. - <a href="/wiki/User:Charles_R_Greathouse_IV">Charles R Greathouse IV</a>, Dec 09 2012</div> <div class=sectline>a(n) = <a href="/A219996" title="Centuries whose prime pattern is the same as prime pattern in the previous century.">A219996</a>(n) - 1. - <a href="/wiki/User:V._Raman">V. Raman</a>, Dec 09 2012</div> </div> </div> <div class=section> <div class=sectname>EXAMPLE</div> <div class=sectbody> <div class=sectline>The first value refers to two consecutive prime-free centuries (cf. <a href="/A181098" title="Primefree centuries (i.e., numbers k such that no prime exists between 100*k and 100*k+99).">A181098</a>); the second value is such that 100*a(2)+17 and 100*a(2)+117 are the only primes between 100*a(2) and 100*(a(2)+2). See the link for more examples.</div> </div> </div> <div class=section> <div class=sectname>CROSSREFS</div> <div class=sectbody> <div class=sectline>Cf. <a href="/A181098" title="Primefree centuries (i.e., numbers k such that no prime exists between 100*k and 100*k+99).">A181098</a>.</div> <div class=sectline>Cf. <a href="/A219996" title="Centuries whose prime pattern is the same as prime pattern in the previous century.">A219996</a> (upper century).</div> <div class=sectline>Sequence in context: <a href="/A164973" title="Theta series of a possible dual-extremal lattice of level 2 and dimension 52.">A164973</a> <a href="/A114673" title="Primes with 57 as smallest positive primitive root.">A114673</a> <a href="/A251370" title="Number of (n+1)X(5+1) 0..2 arrays with every 2X2 subblock summing to 1 2 3 4 5 6 or 7">A251370</a> * <a href="/A228271" title="Prime-free centuries such that the next century is also prime-free.">A228271</a> <a href="/A219996" title="Centuries whose prime pattern is the same as prime pattern in the previous century.">A219996</a> <a href="/A183659" title="Number of (n+1)X7 0..5 arrays with every 2x2 subblock summing to 10">A183659</a></div> <div class=sectline>Adjacent sequences: <a href="/A190636" title="a(n)=(n^3+3*n^7)/4.">A190636</a> <a href="/A190637" title="Primes p == 3 mod 4 whose index as prime divides their index as a Gaussian prime (in the first quadrant, as defined in A1034...">A190637</a> <a href="/A190638" title="Numbers n such that with b=n*(2n-1) two remainders x and y are defined via x = 2^(b-1) -1 mod b and y = (2*n-1)^(b-1) - 1 mo...">A190638</a> * <a href="/A190640" title="Numbers whose base-3 expansion ends in 2 and does not contain any 1's.">A190640</a> <a href="/A190641" title="Numbers having exactly one non-unitary prime factor.">A190641</a> <a href="/A190642" title="Numbers 3n+2 written in base 3.">A190642</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:M._F._Hasler">M. F. Hasler</a>, May 15 2011</div> </div> </div> <div class=section> <div class=sectname>EXTENSIONS</div> <div class=sectbody> <div class=sectline>a(1)-a(5) computed by J. K. Andersen, May 15 2011</div> <div class=sectline>a(6)-a(30) from <a href="/wiki/User:Donovan_Johnson">Donovan Johnson</a>, May 15 2011</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 February 17 21:56 EST 2025. Contains 380976 sequences.</div> <div class=legal> <a href="/wiki/Legal_Documents">License Agreements, Terms of Use, Privacy Policy</a> </div> </div> </center> </div> </body> </html>