A324219 - OEIS

%I #13 Jan 11 2020 15:57:47

%S 1,1,1,2,13,3638334640025

%N Number of digits in 3^^n.

%C Next term is too large to fit in the data section.

%C 3^^n is _Don Knuth_'s up arrow notation for the power tower 3^3^...^3 (with n threes).

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/KnuthUp-ArrowNotation.html">Knuth's Up Arrow Notation</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Tetration">Tetration</a>

%e 3^^-1=0, so a(-1)=1;

%e 3^^0=1, so a(0)=1;

%e 3^^1=3, so a(1)=1;

%e 3^^2=27, so a(2)=2;

%e 3^^3=7625597484987, so a(3)=13;

%e 3^^4 = 3^(3^(3^3)) = ...

%Y Cf. A319898.

%K nonn,base

%O -1,4

%A _Natan Arie Consigli_, Feb 18 2019