A243913 Decimal expansion of 9^(9^(9^9)) = 9^^4.

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

Offset

1,1

Comments

The offset is 1 because the true offset would be 10^(4.085349171835445 * 10^369693099), which is too large to be written out in full in the OEIS or, for that matter, the Universe.

9^8^7^6^5^4^3^2^1^0 (mod 100000000) = 79806721; 9^8^7^6^5^4^3^2^1^0 = 10^10^10^10^(4.829261035877073 * 10^183230).

References

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

Links

Hans Havermann and Robert G. Wilson v, Table of n, a(n) for n = 1..10000

Robert P. Munafo, Hyper4 Iterated Exponential Function

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

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

Formula

9^(9^(9^9)) = ((((( ... 387420478 ... (((((9^9)^9)^9)^9)^9) ... 387420478 ... ^9)^9)^9)^9)^9)^9.

Example

=2141983294796805611333364373442480830147227072845128488706516195982808749656704847036118447249917368...(4.085349171835445... * 10^369693099) ... 3771540670946945552331518959254852001991324340257630363975097419408973491530163140828233401045865289.
The first and last 100 digits are shown above, with the intervening digits omitted. The final one hundred digits cannot be computed with: PowerMod[9, 9^9^9, 10^100] with any version of Mathematica before version 9. Instead (* Import Mmca coding for "SuperPowerMod" and "LogStar" from text file and then *) SuperPowerMod[9, 4, 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, 9^9^9] (* needs version 9.0 to run *)

Crossrefs

Cf. A002488, A054382, A085667, A202955, A054382, A014221, A241291, A241292, A241293, A241294, A241295, A241296, A241297, A241298, A241299.

Sequence in context: A146418 A146011 A104620 * A186724 A145930 A145762

Adjacent sequences: A243910 A243911 A243912 * A243914 A243915 A243916

Keyword

nonn,cons,fini,hard

Author

Hans Havermann and Robert G. Wilson v, Jun 14 2014

Extensions

Keyword: fini added by Jianing Song, Sep 18 2019

Status

approved