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 A144541 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 13^A(k) == A(k) mod 10^k. 16

%I

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

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

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

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

%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="/A144541/b144541.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 350540552884591812248887692071686904673235689443665663593170433746147669728547...

%t (* Import Mmca coding for "SuperPowerMod" and "LogStar" from text file in A133612 and then *) \$RecursionLimit = 2^14; f[n_] := SuperPowerMod[13, 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, A144542, A144543, A144544.

%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

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Last modified June 16 11:47 EDT 2019. Contains 324152 sequences. (Running on oeis4.)