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%I #22 Sep 20 2019 12:28:52
%S 4,4,4,6,2,3,5,1,9,0,2,3,6,9,3,4,6,9,7,5,2,5,6,5,8,2,2,2,8,2,9,2,0,0,
%T 1,5,4,0,5,7,9,4,1,4,5,4,2,4,6,3,9,6,6,3,4,2,7,8,2,6,1,5,6,9,4,4,6,3,
%U 1,4,6,6,9,7,2,3,2,2,9,7,7,5,8,4,9,2,9,4,3,0,5,0,4,8,2,1,9,1,9,3,2,6,3,7,4
%N Decimal expansion of 6^(6^(6^6)) = 6^^4.
%C The offset is 1 because the true offset would be 2.069197376... * 10^36305, which is too large to be represented properly in the OEIS.
%H Robert P. Munafo, <a href="http://mrob.com/pub/math/hyper4.html"> Hyper4 Iterated Exponential Function.</a>.
%F 6^(6^(6^6)) = ((((( ... 46645 ... (((((6^6)^6)^6)^6)^6) ... 46645 ... ^6)^6)^6)^6)^6)^6.
%e 4446235190236934697525658222829200154057941454246396634278261569446314669723229775849294305048219193...(2.069197376... * 10^36305)...1753131067593004473155552781300975310520790674421755277191077815819279193580406457883859420138438656.
%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[6, 6^6^6, 10^100].
%t nbrdgt = 105; f[base_, exp_] := RealDigits[ 10^FractionalPart[ N[ exp*Log10[ base], nbrdgt + Floor[ Log10[ exp]] + 2]], 10, nbrdgt][[1]]; f[ 6, 6^6^6] (* Program fixed by _Jianing Song_, Sep 18 2019 *)
%Y Cf. A085667, A202955, A054382, A014221, A241291, A241292, A241293, A241294, 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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