

A211667


Number of iterations sqrt(sqrt(sqrt(...(n)...))) such that the result is < 2.


3



0, 1, 1, 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, 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, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3
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OFFSET

1,4


COMMENTS

Different from A001069, but equal for n < 256.


LINKS



FORMULA

a(2^(2^n)) = a(2^(2^(n1))) + 1, for n >= 1.
G.f.: g(x) = 1/(1x)*Sum_{k>=0} x^(2^(2^k))
= (x^2 + x^4 + x^16 + x^256 + x^65536 + ...)/(1  x).


EXAMPLE

a(n) = 1, 2, 3, 4, 5, ... for n = 2^1, 2^2, 2^4, 2^8, 2^16, ..., i.e., n = 2, 4, 16, 256, 65536, ... = A001146.


MATHEMATICA

a[n_] := Length[NestWhileList[Sqrt, n, # >= 2 &]]  1; Array[a, 100] (* Amiram Eldar, Dec 08 2018 *)


PROG

(PARI) apply( A211667(n, c=0)={while(n>=2, n=sqrtint(n); c++); c}, [1..50]) \\ This defines the function A211667. The apply(...) provides a check and illustration.  M. F. Hasler, Dec 07 2018


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



