

A002488


a(n) = n^(n^n).
(Formerly M5031 N2171)


18




OFFSET

1,4


COMMENTS

Regardless of whether one sets 0^0=1 or 0^0=0 we have a(0)=0.
Number of digits in terms n>3: 155 (n=4), 2185 (n=5), 36306 (n=6), 695975 (n=7), 15151336 (n=8)
This sequence can also be written as H_4(n,3) in standard hyperoperation notation or as (n "uparrow"(2) 3) in Knuth uparrow notation. For more info on hyperoperations see A054871.
First four terms in base 36 are 0, 1, g, 2pb5fusor.  Vladimir Joseph Stephan Orlovsky, Jun 15 2011
Next term in base 36 is 14PLKI42MDV1MT36I2RNAK3GINNT5VCX207HPUF9X0VJ6I1I7H29NU12WLS3ULFV1YYABI94UA3WAUAMSXZ4SNWV27FYA36HQDJ4.  Alonso del Arte, Jul 01 2012
0^^3 = 0 since 0^^k = 1 for even k, 0 for odd k, k >= 0.  Daniel Forgues, May 18 2013


REFERENCES

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).


LINKS

Table of n, a(n) for n=1..3.
Hans Havermann, Next 5 terms
P. Rossier, Grands nombres, Elemente der Mathematik, 3 (1948), 20.
Eric Weisstein's World of Mathematics, Joyce Sequence
Wikipedia, Knuth's uparrow notation


FORMULA

a(n) = H_4(n,3);


EXAMPLE

a(3) = H_4(3,3) = 3^3^3 = 3^27 = 7625597484987.


MAPLE

seq(n^(n^n), n=0..5); # Robert Israel, May 05 2015


MATHEMATICA

Table[If[n == 0, 0, n^n^n], {n, 0, 4}] (* Vladimir Joseph Stephan Orlovsky, Nov 01 2009 *)


PROG

(PARI) a(n)=n^n^n \\ Charles R Greathouse IV, Mar 10 2011
(Sage) [n^(n^n) for n in (1..4)] # Bruno Berselli, May 03 2015


CROSSREFS

Cf. A002489, A054382.
Sequence in context: A058418 A291908 A059933 * A243776 A198631 A185685
Adjacent sequences: A002485 A002486 A002487 * A002489 A002490 A002491


KEYWORD

sign,nice


AUTHOR

N. J. A. Sloane


EXTENSIONS

a(1) prepended by Natan Arie' Consigli, May 02 2015
Hyperoperator notation by Natan Arie' Consigli, Jan 19 2016


STATUS

approved



