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A049384 a(0)=1, a(n+1) = (n+1)^a(n). 13
1, 1, 2, 9, 262144 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

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

REFERENCES

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

LINKS

Table of n, a(n) for n=0..4.

David Applegate, Marc LeBrun, N. J. A. Sloane, Descending Dungeons, Problem 11286, Amer. Math. Monthly, 116 (2009) 466-467.

David Applegate, Marc LeBrun and N. J. A. Sloane, Descending Dungeons and Iterated Base-Changing, arXiv:math.NT/0611293, 2006-2007.

Walter Arrighetti, LabCEM, Department of Electronic Engineering, Univ. degli Studi di Roma "La Sapienza".

Walter Arrighetti, Double Vision [Broken link]

Vladimir Orlovsky, Very Big Number, Feb 19 1999

J. Sondow, MathWorld: Exponential Factorial

J. Sondow, Irrationality measures, irrationality bases, and a theorem of Jarnik, arXiv:math/0406300 [math.NT], 2004; see L_4 in Example 4.

Wikipedia, Exponential factorial

Wikipedia, Liouville number

EXAMPLE

a(4) = 4^9 = 262144.

a(5) = 5^262144 has 183231 decimal digits. - Rick L. Shepherd, Feb 15 2002

a(5) = ~6.2060698786608744707483205572846793 * 10^183230. - Robert G. Wilson v, Oct 24 2015

MATHEMATICA

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 *)

PROG

(PARI) a(n)=if(n>1, n^a(n-1), 1) \\ Charles R Greathouse IV, Sep 13 2013

CROSSREFS

Cf. A000142, A080219, A140319.

Sequence in context: A028581 A030252 * A132859 A103562 A140319 A120314

Adjacent sequences:  A049381 A049382 A049383 * A049385 A049386 A049387

KEYWORD

nonn,changed

AUTHOR

Marcel Jackson (Marcel.Jackson(AT)utas.edu.au)

STATUS

approved

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Last modified June 18 14:29 EDT 2018. Contains 305558 sequences. (Running on oeis4.)