This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A211663 #12 May 14 2025 01:13:28
%S A211663 1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,
%T A211663 3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,
%U A211663 3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3
%N A211663 Number of iterations log(log(log(...(n)...))) such that the result is < 1.
%C A211663 Same as A211661 for n < 16.
%F A211663 With the exponentiation definition E_{i=1..n} c(i) := c(1)^(c(2)^(c(3)^(...(c(n-1)^(c(n)))...))); E_{i=1..0} := 1; example: E_{i=1..4} 3 = 3^(3^(3^3)) = 3^(3^27), we get:
%F A211663 a(ceiling(E_{i=1..n} e)) = a(ceiling(E_{i=1..n-1} e))+1, for n>=1.
%F A211663 G.f.: g(x) = (1/(1-x))*Sum_{k>=0} x^(ceiling(E_{i=1..k} e)). The explicit first terms of the g.f. are g(x) = (x + x^3 + x^16 + x^3814280 + ...)/(1-x).
%e A211663 a(n)=1, 2, 3, 4, for n=1, ceiling(e), ceiling(e^e), ceiling(e^e^e), = 1, 3, 16, 3814280, respectively.
%Y A211663 Cf. A001069, A010096, A211662, A211664, A211666, A211668, A211669.
%K A211663 base,nonn
%O A211663 1,3
%A A211663 _Hieronymus Fischer_, Apr 30 2012