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A171990 Least integer a(n) for which the iterated function log, iterated n times, is defined. 0
1, 2, 3, 16, 3814280 (list; graph; refs; listen; history; text; internal format)
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
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
Sequence in context: A290590 A263802 A005273 * A103898 A140383 A029913
KEYWORD
nonn
AUTHOR
Alexis Monnerot-Dumaine (alexis.monnerotdumaine(AT)gmail.com), Jan 21 2010
STATUS
approved

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Last modified February 23 19:35 EST 2024. Contains 370283 sequences. (Running on oeis4.)