The OEIS is supported by the many generous donors to the OEIS Foundation.

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 60, we have over 367,000 sequences, and we’ve crossed 11,000 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS Different from A001069, but equal for n < 256. LINKS Amiram Eldar, Table of n, a(n) for n = 1..10000 FORMULA a(2^(2^n)) = a(2^(2^(n-1))) + 1, for n >= 1. G.f.: g(x) = 1/(1-x)*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 (Python) A211667=lambda n: n and (n.bit_length()-1).bit_length() # Nathan L. Skirrow, May 16 2023 CROSSREFS Cf. A001069, A001146, A010096, A211662, A211668, A211670. Sequence in context: A151659 A057467 A074594 * A001069 A156877 A110591 Adjacent sequences: A211664 A211665 A211666 * A211668 A211669 A211670 KEYWORD nonn AUTHOR Hieronymus Fischer, Apr 30 2012 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 1 23:26 EST 2023. Contains 367503 sequences. (Running on oeis4.)