This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A206636 #38 Jan 08 2025 10:42:52 %S A206636 6,36,736,8736,48736,948736,2948736,32948736,432948736,3432948736, %T A206636 53432948736,353432948736,5353432948736,75353432948736,75353432948736, %U A206636 5075353432948736,15075353432948736,615075353432948736,8615075353432948736,98615075353432948736,98615075353432948736,8098615075353432948736 %N A206636 a(n) = 2^^(n+2) modulo 10^n, where ^^ denotes a power tower (see A133612). %C A206636 Backward concatenation of A133612. %C A206636 For all m>n+1, 2^^m == 2^^(n+2) (mod 10^n). Hence, each term represents the trailing decimal digits of 2^^m for every sufficiently large m. %D A206636 M. Ripà, La strana coda della serie n^n^...^n, Trento, UNI Service, Nov 2011. ISBN 978-88-6178-789-6. %H A206636 Robert G. Wilson v, <a href="/A206636/b206636.txt">Table of n, a(n) for n = 1..1000</a> %H A206636 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. %H A206636 Robert G. Wilson v, <a href="/A133612/a133612_2.txt">Mathematica coding for "SuperPowerMod" from Vardi</a> %F A206636 a(n) = A014221(n+3) mod (10^n). %F A206636 For n>1, a(n) = 2^a(n-1) mod 10^n. %t A206636 (* first load all lines of Super Power Mod by Ilan Vardi from the hyper-link, then *) $RecursionLimit = 2^14; a[n_] := SuperPowerMod[2, n +2, 10^n]; Array[a, 22] (* _Robert G. Wilson v_, Apr 20 2020 *) %Y A206636 Cf. A133612, A113627, A109405, A133613, A133614, A133615, A133616, A133617, A133618, A133619, A183613, A144539, A144540, A144541, A144542, A144543, A144544. %K A206636 nonn %O A206636 1,1 %A A206636 _Marco Ripà_, Feb 10 2012