%I #18 Mar 06 2014 18:21:58
%S 6,1,6,5,1,4,0,9,2,0,5,9,4,0,5,7,0,1,8,7,6,6,3,2,8,6,2,2,5,8,4,6,2,0,
%T 8,8,3,8,0,0,5,6,9,9,8,2,5,2,1,1,7,8,5,3,3,6,7,3,2,1,7,8,3,7,0,0,2,6,
%U 6,6,2,0,7,0,5,9,0,6,1,7,5,0,9,0,7,1,8,5,0,6,1,3,2,2,0,1,1,1,0,1,7,7,0,2,4
%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 16^A(k) == A(k) mod 10^k.
%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="/A144544/b144544.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), J. Int. Seq. 12 (2009) #09.8.8
%e 616514092059405701876632862258462088380056998252117853367321783700266620705906...
%t (* Import Mmca coding for "SuperPowerMod" and "LogStar" from text file in A133612 and then *) $RecursionLimit = 2^14; f[n_] := SuperPowerMod[16, n + 1, 10^n]; Reverse@ IntegerDigits@ f@ 105 (* _Robert G. Wilson v_, Mar 06 2014 *)
%Y Cf. A133612, A133613, A133614, A133615, A133616, A133617, A133618, A133619, A144539, A144540, A144541, A144542, A144543.
%K nonn,base
%O 0,1
%A _N. J. A. Sloane_, Dec 20 2008
%E a(68) onward from _Robert G. Wilson v_, Mar 06 2014