This site is supported by donations to The OEIS Foundation.



Annual Appeal: Today, Nov 11 2014, is the 4th anniversary of the launch of the new OEIS web site. 70,000 sequences have been added in these four years, all edited by volunteers. Please make a donation (tax deductible in the US) to help keep the OEIS running.

(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A049384 a(0)=1, a(n+1) = (n+1)^a(n). 12
1, 1, 2, 9, 262144 (list; graph; refs; listen; history; text; internal format)



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


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.


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).

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 2004; see L_4 in Example 4.

Wikipedia, Exponential factorial

Wikipedia, Liouville number


a(4) = 4^9 = 262144.

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


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 *)


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


Cf. A000142, A080219, A140319.

Sequence in context: A028581 A030252 * A132859 A103562 A140319 A120314

Adjacent sequences:  A049381 A049382 A049383 * A049385 A049386 A049387




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



Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement .

Last modified December 18 18:49 EST 2014. Contains 252174 sequences.