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A096113
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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.
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7
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Another rearrangement of the natural numbers.
Description from R. J. Mathar, Feb 21 2009: (Start) 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). (End)
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LINKS
| R. J. Mathar, Table of n, a(n) for n = 1..385
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EXAMPLE
| 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.
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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]
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CROSSREFS
| Cf. A096111, A052330.
Sequence in context: A109890 A086537 A127562 * A110797 A083872 A121663
Adjacent sequences: A096110 A096111 A096112 * A096114 A096115 A096116
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KEYWORD
| nonn
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AUTHOR
| Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Jun 29 2004
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EXTENSIONS
| Edited by Joel Lewis (jblewis(AT)fas.harvard.edu), Nov 15 2006
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