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

Author

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

Keywords

• nonn
• cons
• fini

Comments

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

Examples

			=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].
		

Links

• Robert P. Munafo, Hyper4 Iterated Exponential Function..

Crossrefs

Cf. A000244, A014222.

Cf. A085667, A202955,

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

Programs

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)]

PARI

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

Formula

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

Extensions

Keyword: fini added by Jianing Song, Sep 18 2019