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%I #30 Jun 28 2023 07:21:51
%S 2,3,6,1,0,2,2,6,7,1,4,5,9,7,3,1,3,2,0,6,8,7,7,0,2,7,4,9,7,7,8,1,7,9,
%T 4,3,0,9,4,6,1,2,7,2,9,1,4,7,7,5,1,5,4,4,6,7,1,9,2,5,6,9,4,6,2,1,2,7,
%U 1,1,8,5,3,6,6,6,4,7,5,5,2,4,9,4,5,7,6,9,3,5,0,1,0,1,9,4,1,9,9,7,7,1,6,1,6
%N Decimal expansion of 4^(4^(4^4)) = 4^^4.
%C The offset is 1 because the true offset would be 8.072304726...*10^153, which is too large to be represented properly in the OEIS.
%C This is the decimal expansion of 2^2^513. - _Jianing Song_, Dec 25 2018
%H Robert P. Munafo, <a href="http://mrob.com/pub/math/hyper4.html"> Hyper4 Iterated Exponential Function.</a>.
%F 4^(4^(4^4)) = ((((( ... 245 ... (((((4^4)^4)^4)^4)^4) ... 245 ... ^4)^4)^4)^4)^4)^4.
%e 2361022671459731320687702749778179430946127291477515446719256946212711853666475524945769350101941997...(8.072304726...*10^153) ... 7470426497333490366540651560537534642789067586985427238232605843019607448189676936860456095261392896.
%e The above 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[4, 4^4^4, 10^100].
%t nbrdgt = 105; f[base_, exp_] := RealDigits[ 10^FractionalPart[ N[ exp*Log10[ base], nbrdgt + Floor[ Log10[ exp]] + 2]], 10, nbrdgt][[1]]; f[ 4, 4^4^4] (* or *)
%t p = 4; f[n_] := Quotient[n^p, 10^(Floor[p * Log10@ n] - (1004 + p^p))]; IntegerDigits@ Quotient[ Nest[ f@ # &, p, p^p], 10^(900 + p^p)] (* Program fixed by _Jianing Song_, Sep 18 2019 *)
%Y Cf. A114561, A085667, A202955, A054382, A014221, A241291, A241292, A241294, A241295, A241296, A241297, A241298, A241299, A243913.
%K nonn,cons,fini
%O 1,1
%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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