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 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 (list; graph; refs; listen; history; text; internal format)
 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. 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 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

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Last modified August 8 18:36 EDT 2020. Contains 336298 sequences. (Running on oeis4.)