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How can I make Mathematica calculate a power tower for a succession of numbers, but instead of writing them, Mathematica does the iterative calculation.

     cal= 99^2^3^-----1000  

How to make mathematics write it and if you can calculate it?

I understand that there may be an overflow of memory upon actual calculation, it can also help me

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  • $\begingroup$ There are two possible implementations on MathWorld. $\endgroup$ – C. E. Nov 11 '19 at 8:01
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You can define

pt[n_] := Power @@ Flatten[{99, Range[2, n]}]

But it won't get you very far

Table[pt[n], {n, 2, 4}]
(* {9801, 9227446944279201, Overflow[]} *)

As a check

{99^2, 99^(2^3), 99^(2^(3^4))}
(* {9801, 9227446944279201, Overflow[]} *)
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  • $\begingroup$ thank , How can I see what mathematics writes (the same as what you put with check) $\endgroup$ – zeros Nov 10 '19 at 18:07
  • $\begingroup$ @zeros Do you just want the formatting? Something like 99^## & @@ HoldForm /@ Range[2, 7] ? $\endgroup$ – Mr.Wizard Nov 10 '19 at 18:20
  • $\begingroup$ @ Mr.Wizard , thanks that is very good, the previous routine could be used, so that it shows them and calculates them simultaneously until the overflow occurs $\endgroup$ – zeros Nov 10 '19 at 18:35
  • $\begingroup$ You could also use Nest[]: Nest[99^# &, 1, 3]. $\endgroup$ – J. M. will be back soon Nov 14 '19 at 23:02

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