This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A133617 #27 Feb 10 2022 22:53:17
%S A133617 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 A133617 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 A133617 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 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).
%C A133617 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 A133617 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 A133617 Ilan Vardi, "Computational Recreations in Mathematica," Addison-Wesley Publishing Co., Redwood City, CA, 1991, pages 226-229.
%H A133617 Robert G. Wilson v, <a href="/A133617/b133617.txt">Table of n, a(n) for n = 0..1024</a>
%H A133617 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 A133617 343271565115562133346358333736086036956741826659265308652844477767549129865770...
%e A133617 Sequences A133612-A144544 generalize the observation that 7^343 == 343 (mod 1000).
%t A133617 (* 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 A133617 Cf. A133612, A133613, A133614, A133615, A133616, A133618, A133619, A144539, A144540, A144541, A144542, A144543, A144544.
%K A133617 nonn,base
%O A133617 0,1
%A A133617 Daniel Geisler (daniel(AT)danielgeisler.com), Dec 18 2007
%E A133617 More terms from J. Luis A. Yebra, Dec 12 2008
%E A133617 Edited by _N. J. A. Sloane_, Dec 22 2008
%E A133617 a(68) onward from _Robert G. Wilson v_, Mar 06 2014