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A241292 The decimal expansion of 3^(3^(3^3)) = 3^^4. 10
1, 2, 5, 8, 0, 1, 4, 2, 9, 0, 6, 2, 7, 4, 9, 1, 3, 1, 7, 8, 6, 0, 3, 9, 0, 6, 9, 8, 2, 0, 3, 2, 8, 1, 2, 1, 5, 5, 1, 8, 0, 4, 6, 7, 1, 4, 3, 1, 6, 5, 9, 6, 0, 1, 5, 1, 8, 9, 6, 7, 4, 9, 4, 4, 3, 8, 1, 2, 1, 1, 0, 1, 1, 3, 0, 0, 0, 1, 7, 7, 8, 5, 3, 1, 0, 8, 0, 3, 9, 0, 3, 2, 9, 6, 2, 4, 0, 1, 1, 5, 6, 9, 5, 8, 5 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

3638334640025,2

LINKS

Table of n, a(n) for n=3638334640025..3638334640129.

Robert P. Munafo, Hyper4 Iterated Exponential Function..

FORMULA

= 3^(3^(3^3)) = ((((( … 16 … (((((3^3)^3)^3)^3)^3) … 16 … ^3)^3)^3)^3)^3)^3.

EXAMPLE

=1258014290627491317860390698203281215518046714316596015189674944381211011300017785310803903296240115…(3638334639825)…5344828628021555146929939999502212249640012905650177570718344711077047886315075206738945776100739387.

The above example line shows the first one hundred decimal digits and the last one hundred digits with the number of unrepresented digits in parenthesis.

The final one hundred digits where computed by: PowerMod[3, 3^3^3, 10^100].

MATHEMATICA

nbrdgt = 105; f[base_, exp_] := RealDigits[ 10^FractionalPart[ N[ exp*Log10[ base], nbrdgt + Floor[ Log10[ exp]] + 2]], 10, nbrdgt][[1]]; f[ 3, 3^3^3] (* or *)

p = 3; f[n_] := Quotient[n^p, 10^(Floor[p * Log10@ n] - (1004 + p^p))]; IntegerDigits@ Quotient[ Nest[ f@ # &, p, p^p], 10^(900 + p^p)]

PROG

(PARI) 3.^3^3^3 \\ Charles R Greathouse IV, Apr 25 2016

CROSSREFS

Cf. A014222, A085667, A202955, A054382, A014221, A241291, A241293, A241294, A241295, A241296, A241297, A241298, A241299.

Sequence in context: A252283 A007571 A062621 * A248510 A322416 A020772

Adjacent sequences:  A241289 A241290 A241291 * A241293 A241294 A241295

KEYWORD

nonn,cons

AUTHOR

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

STATUS

approved

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Last modified February 22 20:30 EST 2019. Contains 320404 sequences. (Running on oeis4.)