A096113 a(1) = 1, a(2) = 2; then all new products of subsets of pre-existing terms, then the first integer not present, and so on.

1, 2, 3, 6, 4, 8, 12, 18, 24, 36, 48, 72, 144, 5, 10, 15, 16, 20, 30, 32, 40, 54, 60, 64, 80, 90, 96, 108, 120, 160, 180, 192, 216, 240, 270, 288, 320, 324, 360, 384, 432, 480, 540, 576, 648, 720, 768, 864, 960, 1080, 1152, 1296, 1440, 1536, 1620, 1728, 1920, 1944

Offset: 1

Author

Amarnath Murthy, Jun 29 2004

Keywords

• nonn

Comments

Another rearrangement of the natural numbers.

Description: the iterative extension of the sequence is a loop over the steps: (i) Select the smallest integer not yet in the sequence and append it. (ii) Compute a set of all products of two or more distinct factors taken from the current, finite version of the sequence. (iii) Remove members from this set that are already in the sequence. Append the sorted list of the numbers in the set to the sequence. Return to (i). - R. J. Mathar, Feb 21 2009

Examples

			a(3) = 3 because all products of {1, 2} are already included. The only new product generated by {1, 2, 3} is 6, then 4 is the first integer which doesn't appear. Then {1, 2, 3, 6, 4} generates 8 (=2*4), 12 (=2*6=3*4), 18 (=3*6), 24 (=6*4=2*3*4), 36 (=2*3*6), 48 (=2*6*4), 72 (=3*6*4) and 144 (=2*3*6*4). Then the next term is 5. And so on.
		

Links

• R. J. Mathar, Table of n, a(n) for n = 1..385

Crossrefs

Cf. A096111, A052330.

Programs

Mathematica

L[1]={1} L[n_]:=L[n]=Join[L[n-1], Complement[Union[Exp[Map[ Total,Log[Subsets[Delete[L[n-1],1]]]]]],L[n-1]],{n}] L[6]

Extensions

Edited by Joel B. Lewis, Nov 15 2006