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%I #49 Jul 20 2021 20:34:28
%S 4,2,8,1,2,4,7,7,3,1,7,5,7,4,7,0,4,8,0,3,6,9,8,7,1,1,5,9,3,0,5,6,3,5,
%T 2,1,3,3,9,0,5,5,4,8,2,2,4,1,4,4,3,5,1,4,1,7,4,7,5,3,7,2,3,0,5,3,5,2,
%U 3,8,8,7,4,7,1,7,3,5,0,4,8,3,5,3,1,9,3,6,6,5,2,9,9,4,3,2,0,3,3,3,7,5,0,6,0
%N Decimal expansion of 9^(9^9) = 9^^3.
%C Decimal expansion of 3^774840978. - _Jianing Song_, Sep 15 2019
%D Ilan Vardi, "Computational Recreations in Mathematica," Addison-Wesley Publishing Co., Redwood City, CA, 1991, pages 226-229.
%H Googlology Wiki, <a href="https://googology.wikia.org/wiki/Tetration#First_digits">First Digits</a>
%H Hans Havermann, <a href="http://chesswanks.com/seq/n%5En%5En/">n^n^n for n=1 to n=5</a>
%H Hans Havermann, <a href="http://chesswanks.com/seq/n%5en%5en/9%5e9%5e9/01">9^9^9, Volume 1, the first x decimal digits, in 1100 pages with 10000 digits per page.</a>
%H Math Forum, "Ask Dr. Math", <a href="http://mathforum.org/library/drmath/view/61451.html">Value of 9^(9^9)?</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 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/JoyceSequence.html">Joyce Sequence</a>
%H Robert G. Wilson v, <a href="/A133612/a133612_2.txt">Mathematica coding for "SuperPowerMod" from Vardi</a>
%F 9^(9^9) = ((((((((9^9)^9)^9)^9)^9)^9)^9)^9)^9.
%e = 42812477317574704803698711593056352133905548224144
%e 35141747537230535238874717350483531936652994320333
%e ... (369,692,900 digits omitted) ...
%e 26170043150602250406601961656994397543610268552663
%e 74036682906190174923494324178799359681422627177289.
%e The first and last 100 digits are shown above, with the intervening digits omitted.
%e The final one hundred digits were computed using PowerMod[9, 9^9, 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] (* or *)
%t f[n_] := Quotient[n^9, 10^(Floor[9*Log10@ n] - 1010)]; Nest[ f@ # &, 9, 9]
%Y Cf. A002488, A054382, A085667, A202955, A054382, A014221, A241291, A241292, A241293, A241294, A241295, A241296, A241297, A241299, A243913.
%K nonn,cons,fini
%O 369693100,1
%A _Robert Munafo_ and _Robert G. Wilson v_, Apr 18 2014
%E Keyword: fini added by _Jianing Song_, Sep 18 2019