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A002489
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n^(n^2) (or (n^n)^n).
(Formerly M5030 N2170)
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43
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1, 1, 16, 19683, 4294967296, 298023223876953125, 10314424798490535546171949056, 256923577521058878088611477224235621321607, 6277101735386680763835789423207666416102355444464034512896, 196627050475552913618075908526912116283103450944214766927315415537966391196809
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| The number of closed binary operations on a set of order n. Labeled groupoids.
Contribution from Robert Munafo (mrob27(AT)gmail.com), Jan 25 2010: (Start)
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). (End)
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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).
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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 (mrob27(AT)gmail.com), Jan 25 2010]
Eric Postpischil Posting to sci.math newsgroup, May 21 1990
Index entries for sequences related to groupoids
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EXAMPLE
| a(3) = 19683 because (3^3)^3 = 3^(3^2) = 19683.
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MATHEMATICA
| Join[{1}, Table[n^n^2, {n, 10}]] (* From Harvey P. Dale, Sep 06 2011 *)
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PROG
| (MAGMA) [n^(n^2): n in [0..10]]; // Vincenzo Librandi, May 13 2011
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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)+A023185(n)
Cf. A002488.
Cf. A001329, A002488, A023813, A076113, A090588
Cf. A000312 [From Robert Munafo (mrob27(AT)gmail.com), Jan 25 2010]
Sequence in context: A159387 A098175 A089232 * A060205 A140597 A017296
Adjacent sequences: A002486 A002487 A002488 * A002490 A002491 A002492
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KEYWORD
| nonn,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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