

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).


16



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
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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(2n1) ~ 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 41:12 (1983), pp 169176.
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[n1]*a[n+1], First[ Complement[ Range[n], A064736]]]; AppendTo[A064736, an]; an); Table[a[n], {n, 1, 62}] (*JeanFrançois Alcover, Aug 07 2012 *)


PROG

(Haskell)
import Data.List (delete)
a064736 n = a064736_list !! (n1)
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



