A211670 Number of iterations (...f_4(f_3(f_2(n))))...) such that the result is < 2, where f_j(x):=x^(1/j).

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.

Links

Table of n, a(n) for n=1..90.

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

Crossrefs

Cf. A001069, A010096, A084558, A211662, A211664, A211666, A211668, A211669.

Sequence in context: A138902 A211668 A255270 * A036452 A356852 A285481

Adjacent sequences: A211667 A211668 A211669 * A211671 A211672 A211673

Keyword

base,nonn

Author

Hieronymus Fischer, Apr 30 2012

Status

approved