A211670 - OEIS

%I #14 May 28 2023 13:01:16

%S 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,

%T 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,

%U 3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3

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

%C Different from A001069, but equal for n < 16.

%F a(2^(n!)) = a(2^((n-1)!))+1, for n>1.

%F 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).

%e 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.

%o (Python)

%o def A084558(n):

%o  i=1

%o  while n: i+=1;n//=i

%o  return(i-1)

%o A211670=lambda n: n and A084558(n.bit_length()-1) # _Nathan L. Skirrow_, May 17 2023

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

%K base,nonn

%O 1,4

%A _Hieronymus Fischer_, Apr 30 2012