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 A133612 #49 Jan 11 2024 21:27:10
%S A133612 6,3,7,8,4,9,2,3,4,3,5,3,5,7,0,5,1,6,8,9,0,8,3,3,3,5,8,9,5,1,0,0,6,2,
%T A133612 7,8,6,9,6,8,2,5,5,4,1,0,7,5,4,2,6,8,2,6,1,4,8,2,8,2,1,2,1,2,1,9,0,7,
%U A133612 2,9,8,3,5,5,8,9,8,9,7,1,0,4,9,0,5,2,2,0,9,1,7,8,8,8,6,5,2,2,4,4,8,3,7,1,0
%N A133612 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 2^A(k) == A(k) (mod 10^k).
%C A133612 10-adic expansion of the iterated exponential 2^^n (A014221) for sufficiently large n (where c^^n denotes a tower of c's of height n). E.g., for n > 9, 2^^n == 2948736 (mod 10^7).
%C A133612 Sequences A133612-A133619 and A144539-A144544 generalize the observation that 7^343 == 343 (mod 1000).
%D A133612 M. Ripà, La strana coda della serie n^n^...^n, Trento, UNI Service, Nov 2011. ISBN 978-88-6178-789-6
%D A133612 Ilan Vardi, "Computational Recreations in Mathematica," Addison-Wesley Publishing Co., Redwood City, CA, 1991, pages 226-229.
%H A133612 Robert G. Wilson v, <a href="/A133612/b133612.txt">Table of n, a(n) for n = 0..5999</a>
%H A133612 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.
%H A133612 Robert G. Wilson v, <a href="/A133612/a133612_2.txt">Mathematica coding for "SuperPowerMod" and associated programs from Prof. Ian Vardi</a> (Corrected Aug 24 2020)
%e A133612 63784923435357051689083335895100627869682554107542682614828212121907298... - _Robert G. Wilson v_, Feb 22 2014
%e A133612 2^36 = 68719476736 == 36 (mod 100), 2^736 == 736 (mod 1000), 2^8736 == 8736 (mod 10000), etc.
%t A133612 (* Import Mmca coding for "SuperPowerMod" and "LogStar" from text file and then *) $RecursionLimit = 2^14; f[n_] := SuperPowerMod[2, n + 1, 10^n]; Reverse@ IntegerDigits@ f@ 105 (* _Robert G. Wilson v_, Feb 22 2014 *)
%Y A133612 Cf. A014221, A109405.
%Y A133612 Cf. A133613, A133614, A133615, A133616, A133617, A133618, A133619, A144539, A144540, A144541, A144542, A144543, A144544.
%K A133612 nonn,base
%O A133612 0,1
%A A133612 Daniel Geisler (daniel(AT)danielgeisler.com), Dec 18 2007
%E A133612 Edited by _N. J. A. Sloane_, Dec 22 2007 and Dec 22 2008
%E A133612 More terms from J. Luis A. Yebra, Dec 12 2008
%E A133612 a(68) onward from _Robert G. Wilson v_, Feb 22 2014