cp's OEIS Frontend

A171990 Least integer a(n) for which the iterated function log, iterated n times, is defined.

%I A171990 #44 Apr 09 2025 14:15:53
%S A171990 1,2,3,16,3814280
%N A171990 Least integer a(n) for which the iterated function log, iterated n times, is defined.
%C A171990 Log(a(1)) is defined if a(1) > 0, so a(1) = 1.
%C A171990 Log(log(a(2))) is defined if log(a(2)) > 0 => a(2) > 1 => a(2) = 2.
%C A171990 The sequence grows rapidly: a(6) = 2.33150...10^1656520, and is too large to include here.
%F A171990 For n > 2, a(n) = ceiling(e^(e^(...))) where e appears n-2 times.
%e A171990 a(2) = 2 because log(log(2)) is defined and log(log(1)) is not;
%e A171990 a(3) = 3 because log(log(log(3))) is defined;
%e A171990 a(4) = 16 because log(log(log(log(16)))) is defined.
%e A171990 From _Robert G. Wilson v_, Jul 05 2022: (Start)
%e A171990 a(3) = ceiling(A001113).
%e A171990 a(4) = ceiling(A073226).
%e A171990 a(5) = ceiling(A073227).
%e A171990 a(6) = ceiling(A085667). (End)
%o A171990 (PARI) a(n) = my(k=1); while(1, my(s=k, i=0); while(s > 0, s=log(s); if(s > 0, i++)); if(i==n-1, return(k)); k++) \\ _Felix Fröhlich_, Nov 22 2015
%Y A171990 Cf. A074785 (log(log(2))), A085667, A004002, A001113, A073226, A073227, A085667.
%K A171990 nonn
%O A171990 1,2
%A A171990 _Alexis Monnerot-Dumaine_, Jan 21 2010