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%I #20 Sep 18 2019 14:03:54
%S 1,2,5,8,0,1,4,2,9,0,6,2,7,4,9,1,3,1,7,8,6,0,3,9,0,6,9,8,2,0,3,2,8,1,
%T 2,1,5,5,1,8,0,4,6,7,1,4,3,1,6,5,9,6,0,1,5,1,8,9,6,7,4,9,4,4,3,8,1,2,
%U 1,1,0,1,1,3,0,0,0,1,7,7,8,5,3,1,0,8,0,3,9,0,3,2,9,6,2,4,0,1,1,5,6,9,5,8,5
%N Decimal expansion of 3^(3^(3^3)) = 3^^4.
%C Decimal expansion of 3^7625597484987. - _Jianing Song_, Sep 15 2019
%H Robert P. Munafo, <a href="http://mrob.com/pub/math/hyper4.html"> Hyper4 Iterated Exponential Function.</a>.
%F = 3^(3^(3^3)) = ((((( ... 16 ... (((((3^3)^3)^3)^3)^3) ... 16 ... ^3)^3)^3)^3)^3)^3.
%e =1258014290627491317860390698203281215518046714316596015189674944381211011300017785310803903296240115...(3638334639825)...5344828628021555146929939999502212249640012905650177570718344711077047886315075206738945776100739387.
%e The above example line shows the first one hundred decimal digits and the last one hundred digits with the number of unrepresented digits in parenthesis.
%e The final one hundred digits where computed by: PowerMod[3, 3^3^3, 10^100].
%t nbrdgt = 105; f[base_, exp_] := RealDigits[ 10^FractionalPart[ N[ exp*Log10[ base], nbrdgt + Floor[ Log10[ exp]] + 2]], 10, nbrdgt][[1]]; f[ 3, 3^3^3] (* or *)
%t p = 3; f[n_] := Quotient[n^p, 10^(Floor[p * Log10@ n] - (1004 + p^p))]; IntegerDigits@ Quotient[ Nest[ f@ # &, p, p^p], 10^(900 + p^p)]
%o (PARI) 3.^3^3^3 \\ _Charles R Greathouse IV_, Apr 25 2016
%Y Cf. A000244, A014222.
%Y Cf. A085667, A202955,
%Y Cf. A054382, A014221, A241291, A241293, A241294, A241295, A241296, A241297, A241298, A241299.
%K nonn,cons,fini
%O 3638334640025,2
%A _Robert Munafo_ and _Robert G. Wilson v_, Apr 18 2014
%E Keyword: fini added by _Jianing Song_, Sep 18 2019
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