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A002488
a(n) = n^(n^n).
(Formerly M5031 N2171)
28
-1, 0, 1, 16, 7625597484987
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 "up-arrow"(2) 3) in Knuth up-arrow 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 14PLKI42MDV1MT36I2RNAK3GINNT5VCX207HPUF9X0VJ6I1I7H29NU\ 12WLS3ULFV1YYABI94UA3WAUAMSXZ4SNWV27FYA36HQDJ4. - 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
Delbert L. Johnson, Table of n, a(n) for n = -1..4
Hans Havermann, Next 5 terms
P. Rossier, Grands nombres, Elemente der Mathematik, Vol. 3 (1948), p. 20; alternative link.
Eric Weisstein's World of Mathematics, Joyce Sequence.
FORMULA
a(n) = H_4(n,3);
Sum_{n>=1} 1/a(n) = A215578. - Amiram Eldar, Nov 11 2020
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
KEYWORD
sign,nice
EXTENSIONS
a(-1) prepended by Natan Arie Consigli, May 02 2015
Hyperoperator notation by Natan Arie Consigli, Jan 19 2016
STATUS
approved