OFFSET
1,2
COMMENTS
Let c be the smallest positive constant such that for all permutations {a_n} of the positive integers, lim inf_{n -> infinity} gcd(a_n, a_{n+1})/n <= c. This sequence shows c >= 1/2.
The definition implies that if a(n) is prime then n is even. - N. J. A. Sloane, May 23 2017
a(2n) ~ n+1 ~ n has asymptotic density 1 and a(2n-1) ~ n(n+1) ~ n^2 has asymptotic density zero. - M. F. Hasler, May 23 2017
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Ray Chandler, Table of n, a(n) for n = 1..200000 (large file, 2.8 MB)
Ray Chandler, Table of n, a(n) for n = 1..2000000 (large gzipped file)
P. Erdős, R. Freud, and N. Hegyvári, Arithmetical properties of permutations of integers, Acta Mathematica Hungarica 41:1-2 (1983), pp. 169-176.
Dana G. Korssjoen, Biyao Li, Stefan Steinerberger, Raghavendra Tripathi, and Ruimin Zhang, Finding structure in sequences of real numbers via graph theory: a problem list, arXiv:2012.04625, Dec 08, 2020
Pierre Mazet, Eric Saias, Etude du graphe divisoriel 4, arXiv:1803.10073 [math.NT], 2018.
MATHEMATICA
A064736 = {a[1]=1, a[2]=2}; a[n_] := a[n] = (an = If[OddQ[n], a[n-1]*a[n+1], First[ Complement[ Range[n], A064736]]]; AppendTo[A064736, an]; an); Table[a[n], {n, 1, 62}] (*Jean-François Alcover, Aug 07 2012 *)
PROG
(Haskell)
import Data.List (delete)
a064736 n = a064736_list !! (n-1)
a064736_list = 1 : 2 : f 1 2 [3..] where
f u v (w:ws) = u' : w : f u' w (delete u' ws) where u' = v * w
-- Reinhard Zumkeller, Mar 23 2012
CROSSREFS
KEYWORD
nonn,easy,nice
AUTHOR
J. C. Lagarias (lagarias(AT)umich.edu), Oct 21 2001
EXTENSIONS
More terms from Vladeta Jovovic, Oct 21 2001
Definition clarified by N. J. A. Sloane, May 23 2017
STATUS
approved