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Initial digit of 3^(3^n) (A055777(n)).
3

%I #20 Aug 12 2023 09:45:18

%S 3,2,1,7,4,8,6,2,2,1,3,3,6,2,1,3,3,4,6,2,2,1,1,1,5,1,2,1,1,7,4,1,1,4,

%T 1,1,1,2,1,1,1,1,1,1,2,1,1,2,2,1,1,1,7,4,8,6,2,1,2,1,3,4,1,1,1,4,8,6,

%U 2,2,1,2,2,1,5,1,6,3,3,4,1,1,2,1,5,1,4,1

%N Initial digit of 3^(3^n) (A055777(n)).

%C This sequence corresponds to the initial digit of 3vvn (since 3^(3^n) = ((((3^3)^3)^...)^3) n-times), where vv indicates weak tetration (see links).

%C The author conjectures that the distribution of the initial digits of the present sequence obey Benford's law or Zipf's law (see links).

%C The corresponding final digit of 3^(3^n) is A010705(n) = 3 if n even or 7 if n odd.

%D A. Iorliam, Natural Laws (Benford's Law and Zipf's Law) For Network Traffic Analysis, In: Cybersecurity in Nigeria. SpringerBriefs in Cybersecurity. Springer, Cham (2019), 3-22. DOI: 10.1007/978-3-030-15210-9_2

%H Pointless Large numbers stuff by Cookiefonster, <a href="https://sites.google.com/site/pointlesslargenumberstuff/home/2/weakoperators">2.03 The Weak Hyper-Operators</a>.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Benford%27s_law">Benford's law</a>.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Zipf%27s_law">Zipf's law</a>.

%F a(n) = floor(3^(3^n)/10^floor(log_10(3^(3^n)))).

%F a(n) = A000030(A055777(n)).

%e a(2) = 1, since 3^(3^2) = 3^9 = 19683.

%t Join[{3},Table[Floor[3^(3^n)/10^Floor[Log10[3^(3^n)]]],{n,16}]]

%Y Cf. A000030, A010705 (last digit), A055777, A364789, A364837.

%K nonn,base

%O 0,1

%A _Marco RipĂ _, Aug 10 2023

%E More terms from _Jinyuan Wang_, Aug 11 2023