A064736 - OEIS (original) (raw)

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

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

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

CROSSREFS

A064745 gives inverse permutation.

AUTHOR

J. C. Lagarias (lagarias(AT)umich.edu), Oct 21 2001