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 A144539 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 11^A(k) == A(k) mod 10^k. 16

%I

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

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

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

%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 11^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="/A144539/b144539.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 116666271978307662027198793432698117510204594399945393924384160568806429261664...

%t (* Import Mmca coding for "SuperPowerMod" and "LogStar" from text file in A133612 and then *) \$RecursionLimit = 2^14; f[n_] := SuperPowerMod[11, 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, A144540, A144541, A144542, A144543, A144544.

%K nonn,base

%O 0,3

%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 17 22:17 EDT 2019. Contains 324200 sequences. (Running on oeis4.)