

A091966


Let f(x)=log x, f^k(x)=f(f^(k1)(x))=f iterated k times at x; a(n) = least k such that f^k(n) <= 1/n.


3



1, 2, 2, 4, 6, 9, 5, 27, 7, 30, 8, 25, 3, 3, 3, 3, 3, 6, 9, 27, 52, 43, 8, 19, 17, 97, 56, 24, 193, 131, 24, 27, 128, 87, 7, 10, 17, 118, 111, 116, 38, 26, 9, 104, 36, 61, 24, 13, 60, 17, 37, 10, 21, 140, 48, 48, 13, 19, 243, 8, 33, 25, 171, 25, 18, 20, 20, 5, 5, 5, 5, 90, 55, 47, 44
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OFFSET

1,2


LINKS



EXAMPLE

log 4 ~= 1.38629 > 1/4
log log 4  ~= 0.32663 > 1/4
log log log 4   ~= 1.11891 > 1/4
log log log log 4    ~= 0.11235 < 1/4. Thus a(4)=4


MATHEMATICA

f[n_] := N[ Abs[ Log[ n]], 1024]; g[n_] := Block[{k = 1}, While[ N[ Nest[f, n, k], 64] > 1/n, k++ ]; k]; Table[ g[n], {n, 75}] (* Robert G. Wilson v, Mar 16 2004 *)


CROSSREFS



KEYWORD

nonn


AUTHOR

J. Taylor (integersfan(AT)yahoo.com), Mar 14 2004


EXTENSIONS



STATUS

approved



