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A377981 - 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>A377981 - OEIS</title> <link rel="search" type="application/opensearchdescription+xml" title="OEIS" href="/oeis.xml"> <script> var myURL = "\/A377981" 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=%2fA377981">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="A377981 - 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> A377981 </div> <div class=seqname> Decimal expansion of G/2 - Pi*log(2)/8, where G = <a href="/A006752" title="Decimal expansion of Catalan's constant 1 - 1/9 + 1/25 - 1/49 + 1/81 - ...">A006752</a>. </div> </div> <div class=scorerefs> 0 </div> </div> <div> <div class=seqdatabox> <div class=seqdata>1, 8, 5, 7, 8, 4, 5, 3, 5, 8, 0, 0, 6, 5, 9, 2, 4, 1, 2, 1, 4, 7, 1, 5, 6, 4, 5, 1, 8, 6, 4, 9, 0, 3, 1, 1, 9, 6, 9, 7, 5, 1, 7, 2, 4, 5, 9, 4, 6, 7, 5, 2, 8, 0, 3, 4, 2, 5, 2, 4, 6, 5, 3, 1, 6, 1, 5, 9, 2, 9, 4, 1, 2, 4, 1, 0, 3, 4, 6, 3, 6, 4, 3, 5, 8, 8, 7, 1, 3, 6, 2, 6, 1, 7, 2, 4, 6, 7, 4, 9</div> <div class=seqdatalinks> (<a href="/A377981/list">list</a>; <a href="/A377981/constant">constant</a>; <a href="/A377981/graph">graph</a>; <a href="/search?q=A377981+-id:A377981">refs</a>; <a href="/A377981/listen">listen</a>; <a href="/history?seq=A377981">history</a>; <a href="/search?q=id:A377981&fmt=text">text</a>; <a href="/A377981/internal">internal format</a>) </div> </div> </div> <div class=entry> <div class=section> <div class=sectname>OFFSET</div> <div class=sectbody> <div class=sectline>0,2</div> </div> </div> <div class=section> <div class=sectname>REFERENCES</div> <div class=sectbody> <div class=sectline>Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 1.7.2, p. 55.</div> </div> </div> <div class=section> <div class=sectname>LINKS</div> <div class=sectbody> <div class=sectline><a href="/A377981/b377981.txt">Table of n, a(n) for n=0..99.</a></div> <div class=sectline>Michael I. Shamos, <a href="http://euro.ecom.cmu.edu/people/faculty/mshamos/cat.pdf">A catalog of the real numbers</a>, (2007). See p. 230.</div> </div> </div> <div class=section> <div class=sectname>FORMULA</div> <div class=sectbody> <div class=sectline>Equals Sum_{n>=0} (-1)^(n+1)/(2*n + 1) Sum_{k=0..n-1} 1/(2*k + 1) (see Finch).</div> <div class=sectline>Equals Integral_{x=0..Pi/4} x*tan(x) dx (see Shamos).</div> <div class=sectline>Equals <a href="/A006752" title="Decimal expansion of Catalan's constant 1 - 1/9 + 1/25 - 1/49 + 1/81 - ...">A006752</a>/2 - <a href="/A102886" title="Decimal expansion of Serret's integral: Integral_{x=0..1} log(x+1)/(x^2+1) dx.">A102886</a>.</div> </div> </div> <div class=section> <div class=sectname>EXAMPLE</div> <div class=sectbody> <div class=sectline>0.18578453580065924121471564518649031196975172459...</div> </div> </div> <div class=section> <div class=sectname>MATHEMATICA</div> <div class=sectbody> <div class=sectline>RealDigits[Catalan/2-Pi Log[2]/8, 10, 100][[1]]</div> </div> </div> <div class=section> <div class=sectname>CROSSREFS</div> <div class=sectbody> <div class=sectline>Cf. <a href="/A006752" title="Decimal expansion of Catalan's constant 1 - 1/9 + 1/25 - 1/49 + 1/81 - ...">A006752</a>, <a href="/A102886" title="Decimal expansion of Serret's integral: Integral_{x=0..1} log(x+1)/(x^2+1) dx.">A102886</a>.</div> <div class=sectline>Sequence in context: <a href="/A265303" title="Decimal expansion of Sum_{k>=1} (x-c(2k-1)), where c = convergents to (x = sqrt(8)).">A265303</a> <a href="/A021925" title="Decimal expansion of 1/921.">A021925</a> <a href="/A227514" title="Decimal expansion of the square root of 2/e.">A227514</a> * <a href="/A305036" title="Number of nX4 0..1 arrays with every element unequal to 0, 1, 2, 6 or 7 king-move adjacent elements, with upper left element...">A305036</a> <a href="/A357106" title="Decimal expansion of the real root of 2*x^3 + x^2 - 2.">A357106</a> <a href="/A119812" title="Decimal expansion of the constant defined by binary sums involving Beatty sequences: c = Sum_{n>=1} A049472(n)/2^n = Sum_{n>...">A119812</a></div> <div class=sectline>Adjacent sequences: <a href="/A377978" title="Total number of coronal tilings for a width one length n straight polyiamond with the T2 triangle.">A377978</a> <a href="/A377979" title="List of exponents in the expansion of (1 - q)*Sum_{n >= 0} q^(2*n*(n+1))*Product_{k >= 2*n+1} 1 - q^k.">A377979</a> <a href="/A377980" title="Lexicographically earliest sequence of distinct nonnegative integers such that for any n >= 0, the binary expansions of A184...">A377980</a> * <a href="/A377982" title="a(n) is the number of terms of A048103 (numbers with no p^p divisors) less than or equal to n.">A377982</a> <a href="/A377983" title="a(n) is the number of terms in the range of A276087 that are <= n, where A276087(n) = A276086(A276086(n)) [the twofold appli...">A377983</a> <a href="/A377984" title="a(n) = 2*sigma(n) - A003961(n), where sigma is the sum of divisors function and A003961 is fully multiplicative function wit...">A377984</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="a decimal expansion of a number"><a href="/A377981/constant">cons</a></span></div> </div> </div> <div class=section> <div class=sectname>AUTHOR</div> <div class=sectbody> <div class=sectline><a href="/wiki/User:Stefano_Spezia">Stefano Spezia</a>, Nov 13 2024</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>