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A038822 - 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>A038822 - OEIS</title> <link rel="search" type="application/opensearchdescription+xml" title="OEIS" href="/oeis.xml"> <script> var myURL = "\/A038822" 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=%2fA038822">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="A038822 - 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> A038822 </div> <div class=seqname> Number of primes between 100n and 100n+99. </div> </div> <div class=scorerefs> 32 </div> </div> <div> <div class=seqdatabox> <div class=seqdata>25, 21, 16, 16, 17, 14, 16, 14, 15, 14, 16, 12, 15, 11, 17, 12, 15, 12, 12, 13, 14, 10, 15, 15, 10, 11, 15, 14, 12, 11, 12, 10, 11, 15, 11, 14, 13, 12, 11, 11, 15, 9, 16, 9, 11, 12, 12, 12, 8, 15, 12, 11, 10, 10, 13, 13, 12, 10, 16, 7, 12, 11, 13, 15, 8, 11, 10, 12, 12, 13, 9, 10</div> <div class=seqdatalinks> (<a href="/A038822/list">list</a>; <a href="/A038822/graph">graph</a>; <a href="/search?q=A038822+-id:A038822">refs</a>; <a href="/A038822/listen">listen</a>; <a href="/history?seq=A038822">history</a>; <a href="/search?q=id:A038822&fmt=text">text</a>; <a href="/A038822/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>The number k first occurs in century <a href="/A186311" title="Least k such that the interval 100k to 100k+99 has exactly n primes.">A186311</a>(k).</div> </div> </div> <div class=section> <div class=sectname>REFERENCES</div> <div class=sectbody> <div class=sectline>George P. Loweke, The Lore of Prime Numbers. New York: Vantage Press (1982): 91.</div> </div> </div> <div class=section> <div class=sectname>LINKS</div> <div class=sectbody> <div class=sectline>T. D. Noe, <a href="/A038822/b038822.txt">Table of n, a(n) for n = 0..9999</a></div> </div> </div> <div class=section> <div class=sectname>FORMULA</div> <div class=sectbody> <div class=sectline>a(n) = pi(100n+99) - pi(100n). - <a href="/wiki/User:Wesley_Ivan_Hurt">Wesley Ivan Hurt</a>, Oct 03 2013</div> </div> </div> <div class=section> <div class=sectname>EXAMPLE</div> <div class=sectbody> <div class=sectline>a(3) = 16 because there are 16 primes between 300 and 399 (namely, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397).</div> <div class=sectline>a(4) = 17 because there are 17 primes between 400 and 499 (401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499).</div> </div> </div> <div class=section> <div class=sectname>MAPLE</div> <div class=sectbody> <div class=sectline>with(numtheory); <a href="/A038822" title="Number of primes between 100n and 100n+99.">A038822</a> := n->pi(100*n+99)-pi(100*n); seq(<a href="/A038822" title="Number of primes between 100n and 100n+99.">A038822</a>(k), k=0..100); # <a href="/wiki/User:Wesley_Ivan_Hurt">Wesley Ivan Hurt</a>, Oct 03 2013</div> </div> </div> <div class=section> <div class=sectname>MATHEMATICA</div> <div class=sectbody> <div class=sectline>Table[PrimePi[100n + 99] - PrimePi[100n], {n, 0, 71}]</div> <div class=sectline>Differences[PrimePi[100 Range[0, 100]]] (* <a href="/wiki/User:Harvey_P._Dale">Harvey P. Dale</a>, Feb 18 2021 *)</div> </div> </div> <div class=section> <div class=sectname>PROG</div> <div class=sectbody> <div class=sectline>(PARI) a(n)=sum(i=100*n, 100*n+99, isprime(i)) \\ <a href="/wiki/User:Charles_R_Greathouse_IV">Charles R Greathouse IV</a>, Apr 28 2015</div> <div class=sectline>(PARI) a(n)= my(r=0, p=100*n, q=p+99); while((p=nextprime(p+1))<=q, r+=isprime(p)); r; \\ <a href="/wiki/User:Ruud_H.G._van_Tol">Ruud H.G. van Tol</a>, Nov 17 2024</div> </div> </div> <div class=section> <div class=sectname>CROSSREFS</div> <div class=sectbody> <div class=sectline>Cf. <a href="/A028505" title="Number of primes <= 100*n.">A028505</a>.</div> <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> (centuries without primes).</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> (centuries having 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).</div> <div class=sectline>Cf. <a href="/A094892" title="a(n) is the number of primes between n*210 and (n+1)*210.">A094892</a>, <a href="/A098592" title="Number of primes between n*30 and (n+1)*30.">A098592</a>.</div> <div class=sectline>Sequence in context: <a href="/A291429" title="The arithmetic function u(n,4,8).">A291429</a> <a href="/A334562" title="E.g.f.: exp(-(x + x^2 + x^3)).">A334562</a> <a href="/A171806" title="Number of 5 X 5 permutation matrices such that the n-th matrix power is the least nonnegative power that gives the identity ...">A171806</a> * <a href="/A375335" title="a(n) is the smallest positive integer whose square can be represented as the sum of n distinct nonzero squares in exactly n ...">A375335</a> <a href="/A061438" title="Number of steps for trajectory of n to reach 1 under the map that sends x -> x/13 if x mod 13 = 0, x -> 14x+13-(x mod 13) if...">A061438</a> <a href="/A022981" title="a(n) = 25-n.">A022981</a></div> <div class=sectline>Adjacent sequences: <a href="/A038819" title="Number of primes less than n*10^10.">A038819</a> <a href="/A038820" title="Number of primes less than n*10^11.">A038820</a> <a href="/A038821" title="Number of primes less than n*10^12.">A038821</a> * <a href="/A038823" title="Number of primes between n*1000 and (n+1)*1000.">A038823</a> <a href="/A038824" title="Number of primes between n*10000 and (n+1)*10000.">A038824</a> <a href="/A038825" title="Number of primes between n*100000 and (n+1)*100000.">A038825</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="edited within the last two weeks">changed</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></div> </div> </div> <div class=section> <div class=sectname>EXTENSIONS</div> <div class=sectbody> <div class=sectline>Edited, corrected and extended by <a href="/wiki/User:Robert_G._Wilson_v">Robert G. Wilson v</a>, Jan 29 2003</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 02:36 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>