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%I A211662 #15 Jun 29 2025 09:01:52
%S A211662 0,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,
%T A211662 2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,
%U A211662 2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2
%N A211662 Number of iterations log_3(log_3(log_3(...(n)...))) such that the result is < 2.
%F A211662 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 A211662 a(E_{i=1..n} 3) = a(E_{i=1..n-1} 3)+1, for n>=1.
%F A211662 G.f.: g(x) = (1/(1-x))*Sum_{k>=1} x^(E_{i=1..k} b(i,k)), where b(i,k)=3 for i<k and b(i,k)=2 for i=k. The explicit first terms of the g.f. are g(x) = (x^2+x^9+x^19683+...)/(1-x).
%e A211662 Records a(n)=0, 1, 2, 3, 4, for n=1, 2, 3^2, 3^3^2, 3^3^3^2 (=1, 2, 9, 3^9 = 19683, 3^19683).
%Y A211662 Cf. A001069, A010096, A211661, A211664, A211666, A211668, A211669.
%K A211662 nonn
%O A211662 1,9
%A A211662 _Hieronymus Fischer_, Apr 30 2012