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

1, 2, 3, 16, 3814280

Offset: 1

Author

Alexis Monnerot-Dumaine, Jan 21 2010

Keywords

• nonn

Comments

Log(a(1)) is defined if a(1) > 0, so a(1) = 1.

Log(log(a(2))) is defined if log(a(2)) > 0 => a(2) > 1 => a(2) = 2.

The sequence grows rapidly: a(6) = 2.33150...10^1656520, and is too large to include here.

Examples

			a(2) = 2 because log(log(2)) is defined and log(log(1)) is not;
a(3) = 3 because log(log(log(3))) is defined;
a(4) = 16 because log(log(log(log(16)))) is defined.
From _Robert G. Wilson v_, Jul 05 2022: (Start)
a(3) = ceiling(A001113).
a(4) = ceiling(A073226).
a(5) = ceiling(A073227).
a(6) = ceiling(A085667). (End)
		

Crossrefs

Cf. A074785 (log(log(2))), A085667, A004002, A001113, A073226, A073227, A085667.

Programs

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

Formula

For n > 2, a(n) = ceiling(e^(e^(...))) where e appears n-2 times.