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A241291 The decimal expansion of 2^(2^(2^(2^(2^2)))) = 2^^6. 10
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, 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, 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 (list; constant; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=1..105.

Robert P. Munafo, Sequence A094358, 2^^N = 1 mod N.

Robert P. Munafo, Hyper4 Iterated Exponential Function.

FORMULA

= 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] (* or *)

p = 2; f[n_] := Quotient[n^p, 10^(Floor[ p*Log10@ n] - (1004 + p^p^p))]; IntegerDigits@ Quotient[ Nest[ f@ # &, p, p^p^p], 10^(900 + p^p^p)]

CROSSREFS

Cf. A014221, A085667, A202955, A054382, A014221, A241292, A241293, A241294, A241295, A241296, A241297, A241298, A241299, A243913.

Sequence in context: A298963 A180760 A233270 * A082995 A079549 A143374

Adjacent sequences:  A241288 A241289 A241290 * A241292 A241293 A241294

KEYWORD

nonn,cons

AUTHOR

Robert Munafo and Robert G. Wilson v, Apr 18 2014

STATUS

approved

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Last modified July 22 09:46 EDT 2018. Contains 312891 sequences. (Running on oeis4.)