A244059 - OEIS

%I #22 Sep 03 2021 05:28:45

%S 1,1,6,1,2,1,4,7,6,2,1

%N Initial digit of the decimal expansion of n^(n^(n^n)) or n^^4 (in Don Knuth's up-arrow notation).

%C This sequence can also be written as (n↑↑4) in Knuth up-arrow notation.

%C 0^^4 = 1 since 0^^k = 1 for even k, 0 for odd k, k >= 0.

%C Conjecture: the distribution of the initial digits obey G. K. Zipf's law.

%H Cut the Knot.org, <a href="http://www.cut-the-knot.org/do_you_know/zipfLaw.shtml">Benford's Law and Zipf's Law</a>, A. Bogomolny, Zipf's Law, Benford's Law from Interactive Mathematics Miscellany and Puzzles.

%H M. E. J. Newman, <a href="http://arxiv.org/abs/cond-mat/0412004">Power laws, Pareto distributions and Zipf's law.</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/JoyceSequence.html">Joyce Sequence</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Knuth&#39;s_up-arrow_notation">Knuth's up-arrow notation</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Zipf&#39;s_law">Zipf's law</a>

%H <a href="/index/Be#Benford">Index entries for sequences related to Benford's law</a>

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

%o (PARI) a(n)=digits(n^n^n^n)[1] \\ impractical for large n; _Charles R Greathouse IV_, May 13 2015

%Y Cf. A241291, A241292, A241293, A241294, A241295, A241296, A241297, A243913, A241299.

%Y Cf. A324220 (number of digits).

%K nonn,base,hard,more

%O 0,3

%A _Robert Munafo_ and _Robert G. Wilson v_, Jun 18 2014