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

1, 2, 3, 16, 3814280

Offset

1,2

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.

Links

Table of n, a(n) for n=1..5.

Formula

a(n) = ceiling(e^(e^...))), n times.

Example

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(e^1 =~     2.7182818284590452353602874...). see A001113.
a(4) = ceiling(e^e =~     1.5154262241479264189760430...*10). see A073226.
a(5) = ceiling(e^e^e =~   3.8142791047602205922092195...*10^6). see A073227.
a(6) = ceiling(e^e^e^e =~ 2.3315043990071954622896899...*10^1656520). see A085667. (End)

Prog

(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

Crossrefs

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

Sequence in context: A290590 A263802 A005273 * A103898 A140383 A029913

Adjacent sequences: A171987 A171988 A171989 * A171991 A171992 A171993

Keyword

nonn

Author

Alexis Monnerot-Dumaine (alexis.monnerotdumaine(AT)gmail.com), Jan 21 2010

Status

approved