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A243913 Decimal expansion of 9^(9^(9^9)) = 9^^4. 9
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 (list; constant; graph; refs; listen; history; text; internal format)
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

Googlology Wiki, Hypercalc

Robert P. Munafo, Hyper4 Iterated Exponential Function

Robert P. Munafo and Kenny T-M Chan, Hypercalc - The Calculator That Doesn't Overflow

Robert P. Munafo and Kenny T-M Chan, Hypercalc

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 *)

PROG

HyperCalc (see the link above): 9^9^9^9

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

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Last modified January 28 06:29 EST 2020. Contains 331317 sequences. (Running on oeis4.)