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A171990
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Least integer a(n) for which the iterated function log, iterated n times, is defined.
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0
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OFFSET
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1,2
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COMMENTS
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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.
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LINKS
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FORMULA
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a(n) = ceiling(e^(e^...))), n times.
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EXAMPLE
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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.
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)
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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Alexis Monnerot-Dumaine (alexis.monnerotdumaine(AT)gmail.com), Jan 21 2010
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STATUS
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approved
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