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%I #35 Jul 19 2021 15:43:41
%S 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 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 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 Decimal expansion of 9^(9^(9^9)) = 9^^4.
%C The offset is 1 because the true offset would be 10^(4.085349171835445 * 10^369693099), which is too large to be written out in full in the OEIS or, for that matter, the Universe.
%C 9^8^7^6^5^4^3^2^1^0 (mod 100000000) = 79806721; 9^8^7^6^5^4^3^2^1^0 = 10^10^10^10^(4.829261035877073 * 10^183230).
%D Ilan Vardi, "Computational Recreations in Mathematica," Addison-Wesley Publishing Co., Redwood City, CA, 1991, pages 226-229.
%H Hans Havermann and Robert G. Wilson v, <a href="/A243913/b243913.txt">Table of n, a(n) for n = 1..10000</a>
%H Robert P. Munafo, <a href="http://mrob.com/pub/math/hyper4.html">Hyper4 Iterated Exponential Function</a>
%H Robert P. Munafo and Robert G. Wilson v, <a href="/A241298/a241298.txt">Mathematica coding for "SuperPowerMod" from Vardi</a>
%H Robert G. Wilson v, <a href="/A133612/a133612_2.txt">Mathematica coding for "SuperPowerMod" from Vardi</a>
%F 9^(9^(9^9)) = ((((( ... 387420478 ... (((((9^9)^9)^9)^9)^9) ... 387420478 ... ^9)^9)^9)^9)^9)^9.
%e =2141983294796805611333364373442480830147227072845128488706516195982808749656704847036118447249917368...(4.085349171835445... * 10^369693099) ... 3771540670946945552331518959254852001991324340257630363975097419408973491530163140828233401045865289.
%e 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 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 Cf. A002488, A054382, A085667, A202955, A054382, A014221, A241291, A241292, A241293, A241294, A241295, A241296, A241297, A241298, A241299.
%K nonn,cons,fini,hard
%O 1,1
%A _Hans Havermann_ and _Robert G. Wilson v_, Jun 14 2014
%E Keyword: fini added by _Jianing Song_, Sep 18 2019