OFFSET
1,4
COMMENTS
From Hieronymus Fischer, Apr 08 2012: (Start)
In terms of A010096 the definition could read: "Number of iterations log_2(log_2(log_2(...(n)...))) such that the result is < 2".
LINKS
T. D. Noe, Table of n, a(n) for n = 1..1000
FORMULA
From Hieronymus Fischer, Apr 08 2012: (Start)
a(n) = A010096(n)-1.
With the exponentiation definition E_{i=1..n} c(i) := c(1)^(c(2)^(c(3)^(...(c(n-1)^(c(n)))...))); E_{i=1..0} := 1; example: E_{i=1..4} 2 = 2^(2^(2^2)) = 2^16, we get:
a(E_{i=1..n} 2) = a(E_{i=1..n-1} 2) +1, for n>=1.
G.f.: g(x) = 1/(1-x)*Sum_{k >= 1} x^(E_{i=1..k} 2).
The explicit first terms of this g.f. are
g(x) = (x^2+x^4+x^16+x^65536+...)/(1-x). (End)
EXAMPLE
a(n)=1, 2, 3, 4, 5, ... for n=2, 2^2, 2^2^2, 2^2^2^2, 2^2^2^2^2, ... =2, 4, 16, 65536, 2^65536, ...
MATHEMATICA
f[n_] := Length@ NestWhileList[ Log[2, #] &, n, # >= 2 &] - 1; Array[f, 105] (* Robert G. Wilson v, Apr 19 2012 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved