cp's OEIS Frontend

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

%I A211670 #19 Jun 02 2025 16:49:53
%S A211670 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 A211670 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 A211670 3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3
%N A211670 Number of iterations (...(f_4(f_3(f_2(n))))...) such that the result is < 2, where f_j(x) := x^(1/j).
%C A211670 Different from A001069, but equal for n < 16.
%F A211670 a(2^(n!)) = a(2^((n-1)!))+1, for n>1.
%F A211670 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 A211670 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 A211670 (Python)
%o A211670 def A084558(n):
%o A211670  i=1
%o A211670  while n: i+=1;n//=i
%o A211670  return(i-1)
%o A211670 A211670=lambda n: n and A084558(n.bit_length()-1) # _Natalia L. Skirrow_, May 17 2023
%Y A211670 Cf. A001069, A010096, A084558, A211662, A211664, A211666, A211668, A211669.
%K A211670 base,nonn
%O A211670 1,4
%A A211670 _Hieronymus Fischer_, Apr 30 2012