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
Examples
= 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].
References
- Ilan Vardi, "Computational Recreations in Mathematica," Addison-Wesley Publishing Co., Redwood City, CA, 1991, pages 226-229.
Links
- 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
Crossrefs
Programs
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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]
Formula
9^(9^9) = ((((((((9^9)^9)^9)^9)^9)^9)^9)^9)^9.
Extensions
Keyword: fini added by Jianing Song, Sep 18 2019
Comments