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a(n) = floor(e^e^ ... ^e), with n e's.
6

%I #22 Jul 20 2024 20:03:13

%S 1,2,15,3814279

%N a(n) = floor(e^e^ ... ^e), with n e's.

%C The next term is too large to include.

%C From _Vladimir Reshetnikov_, Apr 27 2013. (Start)

%C a(4) = 2331504399007195462289689911...2579139884667434294745087021 (1656521 decimal digits in total), given by initial segment of A085667.

%C a(5) has more than 10^10^6 decimal digits.

%C a(6) has more than 10^10^10^6 decimal digits. (end)

%p p:= n-> `if`(n=0, 1, exp(1)^p(n-1)):

%p a:= n-> floor(p(n)):

%p seq(a(n), n=0..3); # _Alois P. Heinz_, Jul 20 2024

%t Floor[NestList[Exp, 1, 3]] (* _Vladimir Reshetnikov_, Apr 29 2013 *)

%o (PARI) A056072(n,f=floor)=f(exp(if(n>0,A056072(n-1,x->x)))) \\ [_M. F. Hasler_, May 01 2013]

%Y Cf. A001113, A004002, A003417, A064107, A159825, A073226, A073227, A085667, A225064, A225053.

%K nonn

%O 0,2

%A _Robert G. Wilson v_, Jul 26 2000