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A133614 - 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>A133614 - OEIS</title> <link rel="search" type="application/opensearchdescription+xml" title="OEIS" href="/oeis.xml"> <script> var myURL = "\/A133614" 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=%2fA133614">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="A133614 - 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> A133614 </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 4^A(k) == A(k) (mod 10^k). </div> </div> <div class=scorerefs> 17 </div> </div> <div> <div class=seqdatabox> <div class=seqdata>6, 9, 8, 8, 2, 7, 1, 1, 4, 0, 9, 2, 5, 5, 5, 2, 0, 3, 2, 2, 6, 3, 9, 4, 9, 5, 3, 1, 4, 3, 9, 3, 1, 2, 0, 6, 5, 7, 5, 6, 3, 4, 2, 1, 3, 5, 2, 6, 0, 6, 2, 9, 5, 4, 0, 6, 6, 0, 7, 5, 9, 5, 6, 9, 0, 6, 1, 4, 6, 8, 8, 3, 8, 3, 6, 4, 8, 8, 0, 5, 2, 3, 0, 3, 2, 6, 2, 5, 4, 1, 1, 1, 9, 0, 9, 8, 0, 8, 1, 4, 3, 1, 0, 1, 8</div> <div class=seqdatalinks> (<a href="/A133614/list">list</a>; <a href="/A133614/graph">graph</a>; <a href="/search?q=A133614+-id:A133614">refs</a>; <a href="/A133614/listen">listen</a>; <a href="/history?seq=A133614">history</a>; <a href="/search?q=id:A133614&fmt=text">text</a>; <a href="/A133614/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 4^^n for sufficiently large n (where c^^n denotes a tower of c's of height n). E.g., for n > 9, 4^^n == 1728896 (mod 10^7).</div> </div> </div> <div class=section> <div class=sectname>REFERENCES</div> <div class=sectbody> <div class=sectline>M. Rip脿, 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="/A133614/b133614.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>698827114092555203226394953143931206575634213526062954066075956906146883836488...</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[4, 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="/A133615" 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...">A133615</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="/A340808" title="Decimal expansion of Product_{primes p == 1 (mod 5)} 1/(1-p^(-4)).">A340808</a> <a href="/A233589" title="Decimal expansion of the continued fraction c(1) +c(1)/(c(2) +c(2)/(c(3) +c(3)/(c(4) +c(4)/....))), where c(i)=(i-1)!.">A233589</a> <a href="/A199282" title="Decimal expansion of x>0 satisfying 3*x^2+x*cos(x)=2.">A199282</a> * <a href="/A255674" title="Decimal expansion of a constant related to the Barnes G-function.">A255674</a> <a href="/A019753" title="Decimal expansion of e/16.">A019753</a> <a href="/A200105" title="Decimal expansion of least x satisfying x^2 - 4*cos(x) = 4*sin(x), negated.">A200105</a></div> <div class=sectline>Adjacent sequences: <a href="/A133611" title="A triangular array of numbers related to factorization and number of parts in Murasaki diagrams.">A133611</a> <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="/A133615" 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...">A133615</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></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 March 3 20:29 EST 2025. Contains 381396 sequences.</div> <div class=legal> <a href="/wiki/Legal_Documents">License Agreements, Terms of Use, Privacy Policy</a> </div> </div> </center> </div> </body> </html>