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A049384
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a(0)=1, a(n+1) = (n+1)^a(n).
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15
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OFFSET
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0,3
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COMMENTS
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An "exponential factorial".
Might also be called the "expofactorial" of n. - Walter Arrighetti (walter.arrighetti(AT)fastwebnet.it), Jan 16 2006
By Liouville's theorem, the exponential factorial constant A080219 = Sum_{n>=1} 1/a(n) is a Liouville number and therefore is transcendental. - Jonathan Sondow, Jun 17 2014
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REFERENCES
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David Applegate, Marc LeBrun and N. J. A. Sloane, Descending Dungeons and Iterated Base-Changing, in "The Mathematics of Preference, Choice and Order: Essays in Honor of Peter Fishburn", edited by Steven Brams, William V. Gehrlein and Fred S. Roberts, Springer, 2009, pp. 393-402.
Underwood Dudley, "Mathematical Cranks", MAA 1992, p. 338.
F. Luca, D. Marques, Perfect powers in the summatory function of the power tower, J. Theor. Nombr. Bordeaux 22 (3) (2010) 703, doi:10.5802/jtnb.740
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LINKS
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Walter Arrighetti, LabCEM, Department of Electronic Engineering, Univ. degli Studi di Roma "La Sapienza".
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EXAMPLE
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a(4) = 4^9 = 262144.
a(5) = ~6.2060698786608744707483205572846793 * 10^183230. - Robert G. Wilson v, Oct 24 2015
a(6) = 6^(5^262144) has 4.829261036048226... * 10^183230 decimal digits. - Jack Braxton, Feb 17 2023
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MAPLE
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a:= proc(n) option remember;
`if`(n=0, 1, n^a(n-1))
end:
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MATHEMATICA
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Expofactorial[0] := 1; Expofactorial[n_Integer] := n^Expofactorial[n - 1]; Table[Expofactorial[n], {n, 0, 4}] (* Walter Arrighetti, Jan 24 2006 *)
nxt[{n_, a_}]:={n+1, (n+2)^a}; Transpose[NestList[nxt, {0, 1}, 4]][[2]] (* Harvey P. Dale, May 26 2013 *)
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PROG
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CROSSREFS
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Cf. A132859 (essentially the same).
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KEYWORD
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nonn
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AUTHOR
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Marcel Jackson (Marcel.Jackson(AT)utas.edu.au)
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STATUS
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approved
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