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 A243913 #43 May 01 2025 08:02:04 %S A243913 2,1,4,1,9,8,3,2,9,4,7,9,6,8,0,5,6,1,1,3,3,3,3,6,4,3,7,3,4,4,2,4,8,0, %T A243913 8,3,0,1,4,7,2,2,7,0,7,2,8,4,5,1,2,8,4,8,8,7,0,6,5,1,6,1,9,5,9,8,2,8, %U A243913 0,8,7,4,9,6,5,6,7,0,4,8,4,7,0,3,6,1,1,8,4,4,7,2,4,9,9,1,7,3,6,8,5,3,4,8,8 %N A243913 Decimal expansion of 9^(9^(9^9)) = 9^^4. %C A243913 The offset is taken to be 1 because the true offset would be 4.085349171835445 * 10^369693099, too large to be written out in full. %D A243913 Ilan Vardi, "Computational Recreations in Mathematica," Addison-Wesley Publishing Co., Redwood City, CA, 1991, pages 226-229. %H A243913 Hans Havermann and Robert G. Wilson v, <a href="/A243913/b243913.txt">Table of n, a(n) for n = 1..10000</a> %H A243913 Robert P. Munafo, <a href="http://mrob.com/pub/math/hyper4.html">Hyper4 Iterated Exponential Function</a> %H A243913 Robert P. Munafo and Robert G. Wilson v, <a href="/A241298/a241298.txt">Mathematica coding for "SuperPowerMod" from Vardi</a> %H A243913 Robert G. Wilson v, <a href="/A133612/a133612_2.txt">Mathematica coding for "SuperPowerMod" from Vardi</a> %F A243913 9^(9^(9^9)) = ((((( ... 387420478 ... (((((9^9)^9)^9)^9)^9) ... 387420478 ... ^9)^9)^9)^9)^9)^9. %e A243913 =2141983294796805611333364373442480830147227072845128488706516195982808749656704847036118447249917368...(4.085349171835445... * 10^369693099) ... 3771540670946945552331518959254852001991324340257630363975097419408973491530163140828233401045865289. %e A243913 The first and last 100 digits are shown above, with the intervening digits omitted. The final one hundred digits cannot be computed with: PowerMod[9, 9^9^9, 10^100] with any version of Mathematica before version 9. Instead (* Import Mmca coding for "SuperPowerMod" and "LogStar" from text file and then *) SuperPowerMod[9, 4, 10^100]. %t A243913 nbrdgt = 105; f[base_, exp_] := RealDigits[ 10^FractionalPart[ N[ exp*Log10[ base], nbrdgt + Floor[ Log10[ exp]] + 2]], 10, nbrdgt][[1]]; f[ 9, 9^9^9] (* needs version 9.0 to run *) %Y A243913 Cf. A002488, A054382, A085667, A202955, A054382, A014221, A241291, A241292, A241293, A241294, A241295, A241296, A241297, A241298, A241299. %K A243913 nonn,cons,fini,hard %O A243913 1,1 %A A243913 _Hans Havermann_ and _Robert G. Wilson v_, Jun 14 2014 %E A243913 Keyword: fini added by _Jianing Song_, Sep 18 2019