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A002489
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a(n) = n^(n^2), or (n^n)^n.
(Formerly M5030 N2170)
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48
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1, 1, 16, 19683, 4294967296, 298023223876953125, 10314424798490535546171949056, 256923577521058878088611477224235621321607, 6277101735386680763835789423207666416102355444464034512896, 196627050475552913618075908526912116283103450944214766927315415537966391196809
(list;
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refs;
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history;
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internal format)
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OFFSET
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0,3
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COMMENTS
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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
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REFERENCES
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John S. Rose, A Course on Group Theory, Camb. Univ. Press, 1978, see p. 6.
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
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Vincenzo Librandi and Michael Lee, Table of n, a(n) for n = 0..26 (Vincenzo Librandi supplied the first 16 terms)
Robert Munafo, Hyper4 Iterated Exponential Function [From Robert Munafo, Jan 25 2010]
Eric Postpischil, Posting to sci.math newsgroup, May 21 1990.
P. Rossier, Grands nombres, Elemente der Mathematik, Vol. 3 (1948), p. 20; alternative link.
Index entries for sequences related to groupoids
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FORMULA
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a(n) = [x^(n^2)] 1/(1 - n*x). - Ilya Gutkovskiy, Oct 10 2017
Sum_{n>=1} 1/a(n) = A258102. - Amiram Eldar, Nov 11 2020
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EXAMPLE
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a(3) = 19683 because (3^3)^3 = 3^(3^2) = 19683.
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MATHEMATICA
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Join[{1}, Table[n^n^2, {n, 10}]] (* Harvey P. Dale, Sep 06 2011 *)
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PROG
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(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
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CROSSREFS
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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, A258102.
Sequence in context: A098175 A089232 A300615 * A060205 A140597 A017296
Adjacent sequences: A002486 A002487 A002488 * A002490 A002491 A002492
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KEYWORD
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nonn,easy,nice
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AUTHOR
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N. J. A. Sloane
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STATUS
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approved
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