A064736 a(1)=1, a(2)=2; for n>0, a(2*n+2) = smallest number missing from {a(1), ... ,a(2*n)}, and a(2*n+1) = a(2*n)*a(2*n+2).

1, 2, 6, 3, 12, 4, 20, 5, 35, 7, 56, 8, 72, 9, 90, 10, 110, 11, 143, 13, 182, 14, 210, 15, 240, 16, 272, 17, 306, 18, 342, 19, 399, 21, 462, 22, 506, 23, 552, 24, 600, 25, 650, 26, 702, 27, 756, 28, 812, 29, 870, 30, 930, 31, 992, 32, 1056, 33, 1122, 34, 1224, 36

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.

Index entries for sequences that are permutations of the natural numbers

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

A064745 gives inverse permutation.

Interleaving of A286290 and A286291. See also A286292, A286293.

Cf. A064764, A210770.

Sequence in context: A113552 A282291 A176352 * A303751 A304531 A304755

Adjacent sequences: A064733 A064734 A064735 * A064737 A064738 A064739

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