A091966 Let f(x)=|log x|, f^k(x)=f(f^(k-1)(x))=f iterated k times at x; a(n) = least k such that f^k(n) <= 1/n.

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

Offset

1,2

Links

Table of n, a(n) for n=1..75.

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

First occurrence in A093079, records in A093081 and their index in A093080.

Sequence in context: A153964 A001010 A357952 * A231187 A055529 A337723

Adjacent sequences: A091963 A091964 A091965 * A091967 A091968 A091969

Keyword

nonn

Author

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

Extensions

More terms from Robert G. Wilson v, Mar 16 2004

Status

approved