A241298 Decimal expansion of 9^(9^9) = 9^^3.

4, 2, 8, 1, 2, 4, 7, 7, 3, 1, 7, 5, 7, 4, 7, 0, 4, 8, 0, 3, 6, 9, 8, 7, 1, 1, 5, 9, 3, 0, 5, 6, 3, 5, 2, 1, 3, 3, 9, 0, 5, 5, 4, 8, 2, 2, 4, 1, 4, 4, 3, 5, 1, 4, 1, 7, 4, 7, 5, 3, 7, 2, 3, 0, 5, 3, 5, 2, 3, 8, 8, 7, 4, 7, 1, 7, 3, 5, 0, 4, 8, 3, 5, 3, 1, 9, 3, 6, 6, 5, 2, 9, 9, 4, 3, 2, 0, 3, 3, 3, 7, 5, 0, 6, 0

Offset

369693100,1

Comments

Decimal expansion of 3^774840978. - Jianing Song, Sep 15 2019

References

Ilan Vardi, "Computational Recreations in Mathematica," Addison-Wesley Publishing Co., Redwood City, CA, 1991, pages 226-229.

Links

Table of n, a(n) for n=369693100..369693204.

Googlology Wiki, First Digits

Hans Havermann, n^n^n for n=1 to n=5

Hans Havermann, 9^9^9, Volume 1, the first x decimal digits, in 1100 pages with 10000 digits per page.

Math Forum, "Ask Dr. Math", Value of 9^(9^9)?

Robert P. Munafo, Hyper4 Iterated Exponential Function

Robert P. Munafo and Robert G. Wilson v, Mathematica coding for "SuperPowerMod" from Vardi

Eric Weisstein's World of Mathematics, Joyce Sequence

Robert G. Wilson v, Mathematica coding for "SuperPowerMod" from Vardi

Formula

9^(9^9) = ((((((((9^9)^9)^9)^9)^9)^9)^9)^9)^9.

Example

= 42812477317574704803698711593056352133905548224144
  35141747537230535238874717350483531936652994320333
  ... (369,692,900 digits omitted) ...
  26170043150602250406601961656994397543610268552663
  74036682906190174923494324178799359681422627177289.
The first and last 100 digits are shown above, with the intervening digits omitted.
The final one hundred digits were computed using PowerMod[9, 9^9, 10^100].

Mathematica

nbrdgt = 105; f[base_, exp_] := RealDigits[ 10^FractionalPart[ N[ exp*Log10[ base], nbrdgt + Floor[ Log10[ exp]] + 2]], 10, nbrdgt][[1]]; f[9, 9^9] (* or *)
f[n_] := Quotient[n^9, 10^(Floor[9*Log10@ n] - 1010)]; Nest[ f@ # &, 9, 9]

Crossrefs

Cf. A002488, A054382, A085667, A202955, A054382, A014221, A241291, A241292, A241293, A241294, A241295, A241296, A241297, A241299, A243913.

Sequence in context: A195347 A200693 A348681 * A019953 A241005 A029841

Adjacent sequences: A241295 A241296 A241297 * A241299 A241300 A241301

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