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A133615 - 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>A133615 - OEIS</title> <link rel="search" type="application/opensearchdescription+xml" title="OEIS" href="/oeis.xml"> <script> var myURL = "\/A133615" 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=%2fA133615">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="A133615 - OEIS"></a> </div> <div class="motdbox"> <div class="motd"> <p>Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).</p> </div> <div class="donate"> <div id="donate-button-container"> <div id="donate-button"></div> <script src="https://www.paypalobjects.com/donate/sdk/donate-sdk.js" charset="UTF-8"></script> <script> PayPal.Donation.Button({ env:'production', hosted_button_id:'SVPGSDDCJ734A', image: { src:'https://www.paypalobjects.com/en_US/i/btn/btn_donateCC_LG.gif', alt:'Donate with PayPal button', title:'PayPal - The safer, easier way to pay online!', } }).render('#donate-button'); </script> </div> <a href="https://oeisf.org/donate/"> <strong>Other ways to Give</strong> </a> </div> </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> A133615 </div> <div class=seqname> Unique sequence of digits a(0), a(1), a(2), ... such that for all k >= 2, the number A(k) := Sum_{n = 0..k-1} a(n)*10^n satisfies 5^A(k) == A(k) (mod 10^k). </div> </div> <div class=scorerefs> 17 </div> </div> <div> <div class=seqdatabox> <div class=seqdata>5, 2, 1, 3, 0, 2, 8, 0, 4, 8, 1, 6, 2, 5, 1, 3, 9, 4, 7, 1, 1, 7, 8, 5, 3, 8, 0, 9, 5, 1, 1, 5, 6, 9, 8, 0, 4, 9, 2, 2, 9, 8, 9, 3, 3, 9, 8, 1, 3, 3, 1, 7, 7, 4, 6, 7, 1, 0, 2, 8, 3, 7, 5, 1, 7, 3, 1, 4, 1, 1, 9, 7, 8, 2, 9, 6, 2, 5, 5, 5, 3, 3, 0, 9, 0, 4, 7, 3, 1, 8, 5, 7, 4, 6, 9, 7, 2, 3, 0, 8, 9, 2, 6, 1, 4</div> <div class=seqdatalinks> (<a href="/A133615/list">list</a>; <a href="/A133615/graph">graph</a>; <a href="/search?q=A133615+-id:A133615">refs</a>; <a href="/A133615/listen">listen</a>; <a href="/history?seq=A133615">history</a>; <a href="/search?q=id:A133615&fmt=text">text</a>; <a href="/A133615/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>10-adic expansion of the iterated exponential 5^^n for sufficiently large n (where c^^n denotes a tower of c's of height n). E.g., for n > 9, 5^^n == 8203125 (mod 10^7).</div> </div> </div> <div class=section> <div class=sectname>REFERENCES</div> <div class=sectbody> <div class=sectline>M. Ripà, La strana coda della serie n^n^...^n, Trento, UNI Service, Nov 2011, p. 69-78. ISBN 978-88-6178-789-6.</div> <div class=sectline>Ilan Vardi, "Computational Recreations in Mathematica," Addison-Wesley Publishing Co., Redwood City, CA, 1991, pages 226-229.</div> </div> </div> <div class=section> <div class=sectname>LINKS</div> <div class=sectbody> <div class=sectline>Robert G. Wilson v, <a href="/A133615/b133615.txt">Table of n, a(n) for n = 0..1024</a></div> <div class=sectline>J. Jimenez Urroz and J. Luis A. Yebra, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL12/Yebra/yebra4.html">On the equation a^x == x (mod b^n)</a>, J. Int. Seq. 12 (2009) #09.8.8.</div> </div> </div> <div class=section> <div class=sectname>EXAMPLE</div> <div class=sectbody> <div class=sectline>521302804816251394711785380951156980492298933981331774671028375173141197829625...</div> </div> </div> <div class=section> <div class=sectname>MATHEMATICA</div> <div class=sectbody> <div class=sectline>(* Import Mmca coding for "SuperPowerMod" and "LogStar" from text file in <a href="/A133612" title="Unique sequence of digits a(0), a(1), a(2), ... such that for all k >= 2, the number A(k) := Sum_{n = 0..k-1} a(n)*10^n sati...">A133612</a> and then *) $RecursionLimit = 2^14; f[n_] := SuperPowerMod[5, n + 1, 10^n]; Reverse@ IntegerDigits@ f@ 105 (* <a href="/wiki/User:Robert_G._Wilson_v">Robert G. Wilson v</a>, Mar 06 2014 *)</div> </div> </div> <div class=section> <div class=sectname>CROSSREFS</div> <div class=sectbody> <div class=sectline>Cf. <a href="/A133612" title="Unique sequence of digits a(0), a(1), a(2), ... such that for all k >= 2, the number A(k) := Sum_{n = 0..k-1} a(n)*10^n sati...">A133612</a>, <a href="/A133613" title="Decimal digits such that for all k >= 1, the number A(k) := Sum_{n = 0..k-1} a(n)*10^n satisfies the congruence 3^A(k) == A(...">A133613</a>, <a href="/A133614" title="Unique sequence of digits a(0), a(1), a(2), ... such that for all k >= 2, the number A(k) := Sum_{n = 0..k-1} a(n)*10^n sati...">A133614</a>, <a href="/A133616" title="Unique sequence of digits a(0), a(1), a(2), ... such that for all k >= 2, the number A(k) := Sum_{n = 0..k-1} a(n)*10^n sati...">A133616</a>, <a href="/A133617" title="Unique sequence of digits a(0), a(1), a(2), ... such that for all k >= 2, the number A(k) := Sum_{n = 0..k-1} a(n)*10^n sati...">A133617</a>, <a href="/A133618" title="Unique sequence of digits a(0), a(1), a(2), ... such that for all k >= 2, the number A(k) := Sum_{n = 0..k-1} a(n)*10^n sati...">A133618</a>, <a href="/A133619" title="Unique sequence of digits a(0), a(1), a(2), ... such that for all k >= 2, the number A(k) := Sum_{n = 0..k-1} a(n)*10^n sati...">A133619</a>, <a href="/A144539" title="Unique sequence of digits a(0), a(1), a(2), .. such that for all k >= 2, the number A(k) := Sum_{n = 0..k-1 } a(n)*10^n sati...">A144539</a>, <a href="/A144540" title="Unique sequence of digits a(0), a(1), a(2), .. such that for all k >= 2, the number A(k) := Sum_{n = 0..k-1 } a(n)*10^n sati...">A144540</a>, <a href="/A144541" title="Unique sequence of digits a(0), a(1), a(2), .. such that for all k >= 2, the number A(k) := Sum_{n = 0..k-1 } a(n)*10^n sati...">A144541</a>, <a href="/A144542" title="Unique sequence of digits a(0), a(1), a(2), .. such that for all k >= 2, the number A(k) := Sum_{n = 0..k-1 } a(n)*10^n sati...">A144542</a>, <a href="/A144543" title="Unique sequence of digits a(0), a(1), a(2), .. such that for all k >= 2, the number A(k) := Sum_{n = 0..k-1 } a(n)*10^n sati...">A144543</a>, <a href="/A144544" title="Unique sequence of digits a(0), a(1), a(2), .. such that for all k >= 2, the number A(k) := Sum_{n = 0..k-1 } a(n)*10^n sati...">A144544</a>.</div> <div class=sectline>Sequence in context: <a href="/A275704" title="Digital root of n + (n+1)^2.">A275704</a> <a href="/A038631" title="Continued fraction expansion of Sum_{k>=1} 1/(2^k - 1).">A038631</a> <a href="/A158625" title="Lower limit of backward value of 5^n.">A158625</a> * <a href="/A136161" title="a(n) = 2*a(n-3) - a(n-6), starting a(0..5) = 0, 5, 2, 1, 3, 1.">A136161</a> <a href="/A350688" title="a(n) = (q^2 - A340116(n)^2)/2^n where q is the next prime after A340116(n).">A350688</a> <a href="/A197383" title="Decimal expansion of least x > 0 having sin(Pi*x/6) = sin(Pi*x/3)^2.">A197383</a></div> <div class=sectline>Adjacent sequences: <a href="/A133612" title="Unique sequence of digits a(0), a(1), a(2), ... such that for all k >= 2, the number A(k) := Sum_{n = 0..k-1} a(n)*10^n sati...">A133612</a> <a href="/A133613" title="Decimal digits such that for all k >= 1, the number A(k) := Sum_{n = 0..k-1} a(n)*10^n satisfies the congruence 3^A(k) == A(...">A133613</a> <a href="/A133614" title="Unique sequence of digits a(0), a(1), a(2), ... such that for all k >= 2, the number A(k) := Sum_{n = 0..k-1} a(n)*10^n sati...">A133614</a> * <a href="/A133616" title="Unique sequence of digits a(0), a(1), a(2), ... such that for all k >= 2, the number A(k) := Sum_{n = 0..k-1} a(n)*10^n sati...">A133616</a> <a href="/A133617" title="Unique sequence of digits a(0), a(1), a(2), ... such that for all k >= 2, the number A(k) := Sum_{n = 0..k-1} a(n)*10^n sati...">A133617</a> <a href="/A133618" title="Unique sequence of digits a(0), a(1), a(2), ... such that for all k >= 2, the number A(k) := Sum_{n = 0..k-1} a(n)*10^n sati...">A133618</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>Daniel Geisler (daniel(AT)danielgeisler.com), Dec 18 2007</div> </div> </div> <div class=section> <div class=sectname>EXTENSIONS</div> <div class=sectbody> <div class=sectline>More terms from J. Luis A. Yebra, Dec 12 2008</div> <div class=sectline>Edited by <a href="/wiki/User:N._J._A._Sloane">N. J. A. Sloane</a>, Dec 22 2008</div> <div class=sectline>a(68) onward from <a href="/wiki/User:Robert_G._Wilson_v">Robert G. Wilson v</a>, Mar 06 2014</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 December 11 22:05 EST 2024. 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