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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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified October 2 02:58 EDT 2023. Contains 365831 sequences. (Running on oeis4.)