Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the 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's_up-arrow_notation">Knuth's up-arrow notation</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Zipf'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