login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A002489 n^(n^2), or (n^n)^n.
(Formerly M5030 N2170)
45
1, 1, 16, 19683, 4294967296, 298023223876953125, 10314424798490535546171949056, 256923577521058878088611477224235621321607, 6277101735386680763835789423207666416102355444464034512896, 196627050475552913618075908526912116283103450944214766927315415537966391196809 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

The number of closed binary operations on a set of order n. Labeled groupoids.

The values of "googol" in base N: "10^100" in base 2 is 2^4=16; "10^100" in base 3 is 3^9=19683, etc. This is N^^3 by the "lower-valued" (left-associative) definition of the hyper4 or tetration operator (see Munafo webpage). - Robert Munafo, Jan 25 2010

n^(n^k) = (((n^n)^n)^...)^n, with k+1 n's, k >= 0. - Daniel Forgues, May 18 2013

REFERENCES

J. S. Rose, A Course on Group Theory, Camb. Univ. Press, 1978, see p. 6.

P. Rossier, Grands nombres, Elemente der Mathematik, 3 (1948), 20.

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

Vincenzo Librandi and Michael Lee, Table of n, a(n) for n = 0..26 (Vincenzo Librandi supplied the first 16 terms)

R. Munafo, Hyper4 Iterated Exponential Function [From Robert Munafo, Jan 25 2010]

Eric Postpischil Posting to sci.math newsgroup, May 21 1990

Index entries for sequences related to groupoids

EXAMPLE

a(3) = 19683 because (3^3)^3 = 3^(3^2) = 19683.

MATHEMATICA

Join[{1}, Table[n^n^2, {n, 10}]] (* Harvey P. Dale, Sep 06 2011 *)

PROG

(MAGMA) [n^(n^2): n in [0..10]]; // Vincenzo Librandi, May 13 2011

(PARI) a(n)=n^(n^2) \\ Charles R Greathouse IV, Nov 20 2012

CROSSREFS

a(n)=A079172(n)+A023814(n)=A079176(n)+A079179(n)

a(n)=A079182(n)+A023813(n)=A079186(n)+A079189(n)

a(n)=A079192(n)+A079195(n)+A079198(n)+A023815(n)

Cf. A002488, A001329, A002488, A023813, A076113, A090588, A000312.

Sequence in context: A283720 A098175 A089232 * A060205 A140597 A017296

Adjacent sequences:  A002486 A002487 A002488 * A002490 A002491 A002492

KEYWORD

nonn,easy,nice

AUTHOR

N. J. A. Sloane.

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy .

Last modified March 27 02:45 EDT 2017. Contains 284144 sequences.