A241292 Decimal expansion of 3^(3^(3^3)) = 3^^4.

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

Offset

3638334640025,2

Comments

Decimal expansion of 3^7625597484987. - Jianing Song, Sep 15 2019

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. A000244, A014222.

Cf. A085667, A202955,

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

Sequence in context: A062621 A306748 A344655 * A366248 A362590 A248510

Adjacent sequences: A241289 A241290 A241291 * A241293 A241294 A241295

Keyword

nonn,cons,fini

Author

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

Extensions

Keyword: fini added by Jianing Song, Sep 18 2019

Status

approved