The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

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