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A133616 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 6^A(k) == A(k) mod 10^k. 16

%I

%S 6,5,6,8,3,2,7,4,4,7,2,2,3,9,5,5,6,9,7,6,7,3,2,1,9,6,0,1,7,5,0,6,0,5,

%T 8,6,9,1,8,0,1,3,7,9,4,6,0,4,4,7,0,4,6,4,0,2,4,6,3,7,8,1,6,7,0,8,5,0,

%U 1,4,3,4,4,4,1,8,5,7,5,9,7,0,0,4,2,9,6,3,4,1,8,9,6,0,9,8,4,5,7,0,3,5,0,8,6

%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 6^A(k) == A(k) mod 10^k.

%C 10-adic expansion of the iterated exponential 6^^n for sufficiently large n (where c^^n denotes a tower of c's of height n). E.g. For n>9, 6^^n == 7238656 (mod 10^7)

%D M. RipĂ , 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="/A133616/b133616.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 656832744722395569767321960175060586918013794604470464024637816708501434441857...

%t (* Import Mmca coding for "SuperPowerMod" and "LogStar" from text file in A133612 and then *) $RecursionLimit = 2^14; f[n_] := SuperPowerMod[6, n + 1, 10^n]; Reverse@ IntegerDigits@ f@ 105 (* _Robert G. Wilson v_, Mar 06 2014 *)

%Y Cf. A133612, A133613, A133614, A133615, A133617, A133618, 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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