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A211670
Number of iterations (...f_4(f_3(f_2(n))))...) such that the result is < 2, where f_j(x):=x^(1/j).
8
0, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3
OFFSET
1,4
COMMENTS
Different from A001069, but equal for n < 16.
FORMULA
a(2^(n!)) = a(2^((n-1)!))+1, for n>1.
G.f.: g(x) = 1/(1-x)*Sum_{k>=1} x^(2^(k!)). The explicit first terms of the g.f. are g(x) = (x^2+x^4+x^64+x^16777216+...)/(1-x).
EXAMPLE
a(n)=1, 2, 3, 4, 5 for n=2^(1!), 2^(2!), 2^(3!), 2^(4!), 2^(5!) =2, 4, 64, 16777216, 16777216^5.
PROG
(Python)
def A084558(n):
i=1
while n: i+=1; n//=i
return(i-1)
A211670=lambda n: n and A084558(n.bit_length()-1) # Nathan L. Skirrow, May 17 2023
KEYWORD
base,nonn
AUTHOR
Hieronymus Fischer, Apr 30 2012
STATUS
approved