A133619 - OEIS

%I #33 Feb 10 2022 22:53:12

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

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

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

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

%C 10-adic expansion of the iterated exponential 9^^n for sufficiently large n (where c^^n denotes a tower of c's of height n). E.g., for n > 9, 9^^n == 2745289 (mod 10^7).

%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="/A133619/b133619.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 982547293795780847016574305627284525700589988740419498868468199262013754161360...

%t (* Import Mmca coding for "SuperPowerMod" and "LogStar" from text file in A133612 and then *) $RecursionLimit = 2^14; f[n_] := SuperPowerMod[9, n + 1, 10^n]; Reverse@ IntegerDigits@ f@ 105 (* _Robert G. Wilson v_, Mar 06 2014 *)

%Y Cf. A306686.

%Y Cf. A133612, A133613, A133614, A133615, A133616, A133617, A133618, 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