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 A133617 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 7^A(k) == A(k) mod 10^k. 17

%I

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

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

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

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

%C 10-adic expansion of the iterated exponential 7^^n for sufficiently large n (where c^^n denotes a tower of c's of height n). E.g. For n>9, 7^^n == 5172343 (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="/A133617/b133617.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 343271565115562133346358333736086036956741826659265308652844477767549129865770...

%e Sequences A133612-A144544 generalize the observation that 7^343 == 343 mod 1000.

%t (* Import Mmca coding for "SuperPowerMod" and "LogStar" from text file in A133612 and then *) \$RecursionLimit = 2^14; f[n_] := SuperPowerMod[7, n + 1, 10^n]; Reverse@ IntegerDigits@ f@ 105 (* _Robert G. Wilson v_, Mar 06 2014 *)

%Y Cf. A133612, A133613, A133614, A133615, A133616, 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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Last modified June 19 00:55 EDT 2019. Contains 324217 sequences. (Running on oeis4.)