OFFSET
0,4
COMMENTS
0^^3 = 0 since 0^^k = 1 for even k, 0 for odd k, k >= 0.
Conjecture: the distribution of the initial digits obey Zipf's law.
The distribution of the first 1000 terms beginning with 1: 302, 196, 124, 91, 72, 46, 71, 53, 45.
LINKS
Robert P. Munafo and Robert G. Wilson v, Table of n, a(n) for n = 0..1000
Cut the Knot.org, Benford's Law and Zipf's Law, A. Bogomolny, Zipf's Law, Benford's Law from Interactive Mathematics Miscellany and Puzzles.
Hans Havermann, Next 5 terms.
M. E. J. Newman, Power laws, Pareto distributions and Zipf's law.
Eric Weisstein's World of Mathematics, Joyce Sequence.
Wikipedia, Knuth's up-arrow notation.
Wikipedia, Zipf's law.
FORMULA
For n > 0, a(n) = floor(t/10^floor(log_10(t))) where t = n^(n^n).
EXAMPLE
a(0) = 0, a(1) = 1, a(2) = 1 because 2^(2^2) = 16, a(3) = 7 because 3^(3^3) = 7625597484987 and its initial digit is 7, etc.
MATHEMATICA
g[n_] := Quotient[n^p, 10^(Floor[ p*Log10@ n] - (1004 + p))]; f[n_] := Block[{p = n}, Quotient[ Nest[ g@ # &, p, p], 10^(1004 + p)]]; Array[f, 105, 0]
CROSSREFS
KEYWORD
nonn,base,easy
AUTHOR
Robert Munafo and Robert G. Wilson v, Apr 18 2014
STATUS
approved