OFFSET
1,1
COMMENTS
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.
2^0 = 1, 2^1 = 2, 2^2 = 4,
2^2^2 = 2^^3 = (2^2)^2 = 16,
2^2^2^2 = 2^^4 = (((2^2)^2)^2)^2 = 65536,
2^(2^(2^(2^2))) = 2^^5 = (((((((((((((((2^2)^2)^2)^2)^2)^2)^2)^2)^2)^2)^2)^2)^2)^2)^2)^2 =
2003529930406846464979072351560255750447825475569751419265016973710894059556311453089506130880933348...(19529 digits)...9087575630505718260979581044520267611188489786293085833548068862693010305614986891826277507437428736.
LINKS
Robert P. Munafo, Sequence A094358, 2^^N = 1 mod N.
Robert P. Munafo, Hyper4 Iterated Exponential Function.
FORMULA
Equals 2^2^2^2^2^2 = 2^^6.
EXAMPLE
2120038728808211984885164691662274630835654230675372483625951752354414565561161040708771008806932213...(10^(6.0312260626165015 * 10^19727))...9087575630505718260979581044520267611188489786293085833548068862693010305614986891826277507437428736.
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.
MATHEMATICA
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]
CROSSREFS
KEYWORD
AUTHOR
Robert Munafo and Robert G. Wilson v, Apr 18 2014
EXTENSIONS
Keyword: fini added by Jianing Song, Sep 18 2019
STATUS
approved