

A244059


Initial digit of the decimal expansion of n^(n^(n^n)) or n^^4 (in Don Knuth's uparrow notation).


1



1, 1, 6, 1, 2, 1, 4, 7, 6, 2, 1
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OFFSET

0,3


COMMENTS

This sequence can also be written as (nāā4) in Knuth uparrow notation.
0^^4 = 1 since 0^^k = 1 for even k, 0 for odd k, k >= 0.
Conjecture: the distribution of the initial digits obey G. K. Zipf's law.


LINKS

Table of n, a(n) for n=0..10.
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.
M. E. J. Newman, Power laws, Pareto distributions and Zipf's law.
Eric Weisstein's World of Mathematics, Joyce Sequence
Wikipedia, Knuth's uparrow notation
Wikipedia, Zipf's law
Index entries for sequences related to Benford's law


EXAMPLE

a(4)=2 because A241293(1)=2.


PROG

(PARI) a(n)=digits(n^n^n^n)[1] \\ impractical for large n; Charles R Greathouse IV, May 13 2015


CROSSREFS

Cf. A241291, A241292, A241293, A241294, A241295, A241296, A241297, A243913, A241299.
Sequence in context: A085552 A002950 A324046 * A121090 A321991 A010135
Adjacent sequences: A244056 A244057 A244058 * A244060 A244061 A244062


KEYWORD

nonn,hard,more,base


AUTHOR

Robert Munafo and Robert G. Wilson v, Jun 18 2014


STATUS

approved



