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%I #28 Feb 10 2022 22:52:56
%S 6,5,8,5,2,2,5,9,8,6,1,4,5,3,0,7,7,5,1,2,5,1,8,0,0,1,5,8,8,5,5,9,0,2,
%T 6,1,3,9,1,1,5,6,2,9,8,3,7,7,2,0,1,5,7,3,8,8,2,6,6,7,0,3,7,5,7,2,7,4,
%U 2,4,4,2,4,3,7,5,8,4,4,2,2,1,3,0,8,8,8,8,7,1,5,9,1,2,0,1,6,0,9,8,0,5,3,3,1
%N 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 8^A(k) == A(k) (mod 10^k).
%C 10-adic expansion of the iterated exponential 8^^n for sufficiently large n (where c^^n denotes a tower of c's of height n). E.g., for n > 9, 8^^n == 5225856 (mod 10^7).
%D M. Ripà, La strana coda della serie n^n^...^n, Trento, UNI Service, Nov 2011, p. 69-78. ISBN 978-88-6178-789-6.
%D Ilan Vardi, "Computational Recreations in Mathematica," Addison-Wesley Publishing Co., Redwood City, CA, 1991, pages 226-229.
%H Robert G. Wilson v, <a href="/A133618/b133618.txt">Table of n, a(n) for n = 0..1024</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)</a>, J. Int. Seq. 12 (2009) #09.8.8.
%e 658522598614530775125180015885590261391156298377201573882667037572742442437584...
%e 8^56 == 56 (mod 100), 8^856 == 856 (mod 1000), ...
%t (* Import Mmca coding for "SuperPowerMod" and "LogStar" from text file in A133612 and then *) $RecursionLimit = 2^14; f[n_] := SuperPowerMod[8, n + 1, 10^n]; Reverse@ IntegerDigits@ f@ 105 (* _Robert G. Wilson v_, Mar 06 2014 *)
%Y Cf. A133612, A133613, A133614, A133615, A133616, A133617, A133619, A144539, A144540, A144541, A144542, A144543, A144544.
%K nonn,base
%O 0,1
%A Daniel Geisler (daniel(AT)danielgeisler.com), Dec 18 2007
%E More terms from J. Luis A. Yebra, Dec 12 2008
%E Edited by _N. J. A. Sloane_, Dec 22 2008
%E a(68) onward from _Robert G. Wilson v_, Mar 06 2014
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