%I #36 Aug 25 2020 00:14:03
%S 6,36,736,8736,48736,948736,2948736,32948736,432948736,3432948736,
%T 53432948736,353432948736,5353432948736,75353432948736,75353432948736,
%U 5075353432948736,15075353432948736,615075353432948736,8615075353432948736,98615075353432948736,98615075353432948736,8098615075353432948736
%N a(n) = 2^^(n+2) modulo 10^n, where ^^ denotes a power tower (see A133612).
%C Backward concatenation of A133612.
%C 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 M. Ripà, La strana coda della serie n^n^...^n, Trento, UNI Service, Nov 2011. ISBN 978-88-6178-789-6.
%H Robert G. Wilson v, <a href="/A206636/b206636.txt">Table of n, a(n) for n = 1..1000</a>
%H 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), J. Int. Seq. 12 (2009) #09.8.8.
%H Robert G. Wilson v, <a href="/A133612/a133612_2.txt">Mathematica coding for "SuperPowerMod" from Vardi</a>
%F a(n) = A014221(n+3) mod (10^n).
%F For n>1, a(n) = 2^a(n-1) mod 10^n.
%t (* 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 Cf. A133612, A113627, A109405, A133613, A133614, A133615, A133616, A133617, A133618, A133619, A183613, A144539, A144540, A144541, A144542, A144543, A144544.
%K nonn
%O 1,1
%A _Marco Ripà_, Feb 10 2012