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A049472 - 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>A049472 - OEIS</title> <link rel="search" type="application/opensearchdescription+xml" title="OEIS" href="/oeis.xml"> <script> var myURL = "\/A049472" 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=%2fA049472">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="A049472 - 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> A049472 </div> <div class=seqname> a(n) = floor(n/sqrt(2)). </div> </div> <div class=scorerefs> 23 </div> </div> <div> <div class=seqdatabox> <div class=seqdata>0, 0, 1, 2, 2, 3, 4, 4, 5, 6, 7, 7, 8, 9, 9, 10, 11, 12, 12, 13, 14, 14, 15, 16, 16, 17, 18, 19, 19, 20, 21, 21, 22, 23, 24, 24, 25, 26, 26, 27, 28, 28, 29, 30, 31, 31, 32, 33, 33, 34, 35, 36, 36, 37, 38, 38, 39, 40, 41, 41, 42, 43, 43, 44, 45, 45, 46, 47</div> <div class=seqdatalinks> (<a href="/A049472/list">list</a>; <a href="/A049472/graph">graph</a>; <a href="/search?q=A049472+-id:A049472">refs</a>; <a href="/A049472/listen">listen</a>; <a href="/history?seq=A049472">history</a>; <a href="/search?q=id:A049472&fmt=text">text</a>; <a href="/A049472/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>For n > 0: <a href="/A006337" title="An "eta-sequence": a(n) = floor( (n+1)*sqrt(2) ) - floor( n*sqrt(2) ).">A006337</a>(n) = number of repeating n's. - <a href="/wiki/User:Reinhard_Zumkeller">Reinhard Zumkeller</a>, Jul 04 2015</div> </div> </div> <div class=section> <div class=sectname>LINKS</div> <div class=sectbody> <div class=sectline>Vincenzo Librandi, <a href="/A049472/b049472.txt">Table of n, a(n) for n = 0..10000</a></div> <div class=sectline>Robbert Fokkink, <a href="https://arxiv.org/abs/2309.01644">The Pell Tower and Ostronometry</a>, arXiv:2309.01644 [math.CO], 2023.</div> <div class=sectline><a href="/index/Be#Beatty">Index entries for sequences related to Beatty sequences</a></div> </div> </div> <div class=section> <div class=sectname>MAPLE</div> <div class=sectbody> <div class=sectline><a href="/A049472" title="a(n) = floor(n/sqrt(2)).">A049472</a>:=n->floor(n/sqrt(2)): seq(<a href="/A049472" title="a(n) = floor(n/sqrt(2)).">A049472</a>(n), n=0..100); # <a href="/wiki/User:Wesley_Ivan_Hurt">Wesley Ivan Hurt</a>, Jun 25 2016</div> </div> </div> <div class=section> <div class=sectname>MATHEMATICA</div> <div class=sectbody> <div class=sectline>Floor[Range[0, 70]/Sqrt[2]] (* <a href="/wiki/User:Harvey_P._Dale">Harvey P. Dale</a>, Aug 22 2011 *)</div> </div> </div> <div class=section> <div class=sectname>PROG</div> <div class=sectbody> <div class=sectline>(Magma) [Floor(n/Sqrt(2)): n in [0..70] ]; // <a href="/wiki/User:Vincenzo_Librandi">Vincenzo Librandi</a>, Aug 23 2011</div> <div class=sectline>(Haskell)</div> <div class=sectline>a049472 = floor . (/ sqrt 2) . fromIntegral</div> <div class=sectline>-- <a href="/wiki/User:Reinhard_Zumkeller">Reinhard Zumkeller</a>, Jul 04 2015</div> <div class=sectline>(PARI) a(n)=sqrtint(n^2\2) \\ <a href="/wiki/User:Charles_R_Greathouse_IV">Charles R Greathouse IV</a>, Sep 02 2015</div> </div> </div> <div class=section> <div class=sectname>CROSSREFS</div> <div class=sectbody> <div class=sectline>First differences give <a href="/A080764" title="First differences of A049472, floor(n/sqrt(2)).">A080764</a>.</div> <div class=sectline>Cf. <a href="/A006337" title="An "eta-sequence": a(n) = floor( (n+1)*sqrt(2) ) - floor( n*sqrt(2) ).">A006337</a>, <a href="/A049474" title="a(n) = ceiling(n/sqrt(2)).">A049474</a>.</div> <div class=sectline>Sequence in context: <a href="/A306726" title="a(n) = Sum_{i=1..n} f_i(0), where f_i is the i-th of all functions that are representable as x^x^...^x with m>=1 x's and par...">A306726</a> <a href="/A188511" title="a(n) = floor(7*n/10).">A188511</a> <a href="/A064488" title="A Beatty sequence: Floor[n*c], where c = A064648 is the sum of the reciprocals of primorials.">A064488</a> * <a href="/A368131" title="a(n) = floor(n * log(4/3) / log(3/2))">A368131</a> <a href="/A125229" title="a(n) = j such that i^j is maximized subject to i+j = n (i >= 0, j >= 0).">A125229</a> <a href="/A213855" title="Least m > 0 such that m! * 4^m >= n!.">A213855</a></div> <div class=sectline>Adjacent sequences: <a href="/A049469" title="Decimal expansion of sin(1).">A049469</a> <a href="/A049470" title="Decimal expansion of cos(1).">A049470</a> <a href="/A049471" title="Decimal expansion of tan(1).">A049471</a> * <a href="/A049473" title="Nearest integer to n/sqrt(2).">A049473</a> <a href="/A049474" title="a(n) = ceiling(n/sqrt(2)).">A049474</a> <a href="/A049475" title="Number of 2n X 2n matrices whose entries are {0,-1,+1} and whose row sums and column sums are all distinct.">A049475</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></div> </div> </div> <div class=section> <div class=sectname>AUTHOR</div> <div class=sectbody> <div class=sectline><a href="/wiki/User:Thomas_Kellar">Thomas Kellar</a></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 April 10 10:46 EDT 2025. Contains 382672 sequences.</div> <div class=legal> <a href="/wiki/Legal_Documents">License Agreements, Terms of Use, Privacy Policy</a> </div> </div> </center> </div> </body> </html>