%I #25 Sep 20 2019 12:29:03
%S 2,1,2,0,0,3,8,7,2,8,8,0,8,2,1,1,9,8,4,8,8,5,1,6,4,6,9,1,6,6,2,2,7,4,
%T 6,3,0,8,3,5,6,5,4,2,3,0,6,7,5,3,7,2,4,8,3,6,2,5,9,5,1,7,5,2,3,5,4,4,
%U 1,4,5,6,5,5,6,1,1,6,1,0,4,0,7,0,8,7,7,1,0,0,8,8,0,6,9,3,2,2,1,3,9,7,3,7,3
%N Decimal expansion of 2^(2^(2^(2^(2^2)))) = 2^^6.
%C The offset is 1 because the true offset would be 6.0312260626165015 * 10^19727, which is too large to be represented properly in the OEIS.
%C 2^0 = 1, 2^1 = 2, 2^2 = 4,
%C 2^2^2 = 2^^3 = (2^2)^2 = 16,
%C 2^2^2^2 = 2^^4 = (((2^2)^2)^2)^2 = 65536,
%C 2^(2^(2^(2^2))) = 2^^5 = (((((((((((((((2^2)^2)^2)^2)^2)^2)^2)^2)^2)^2)^2)^2)^2)^2)^2)^2 =
%C 2003529930406846464979072351560255750447825475569751419265016973710894059556311453089506130880933348...(19529 digits)...9087575630505718260979581044520267611188489786293085833548068862693010305614986891826277507437428736.
%H Robert P. Munafo, <a href="http://www.mrob.com/pub/math/seq-a094358.html">Sequence A094358, 2^^N = 1 mod N</a>.
%H Robert P. Munafo, <a href="http://mrob.com/pub/math/hyper4.html">Hyper4 Iterated Exponential Function</a>.
%F Equals 2^2^2^2^2^2 = 2^^6.
%e 2120038728808211984885164691662274630835654230675372483625951752354414565561161040708771008806932213...(10^(6.0312260626165015 * 10^19727))...9087575630505718260979581044520267611188489786293085833548068862693010305614986891826277507437428736.
%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 parentheses.
%t nbrdgt = 105; f[base_, exp_] := RealDigits[ 10^FractionalPart[ N[ exp*Log10[ base], nbrdgt + Floor[ Log10[ exp]] + 2]], 10, nbrdgt][[1]]; f[2, 2^2^2^2^2]
%Y Cf. A014221, A085667, A202955, A054382, A014221, A241292, A241293, 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