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A096063
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Beginning with the sequence S(1)={1} form, in succession, the sequence S(n) for n=2,3,4,... by inserting the n smallest multiples of n that have not been used previously, in order of increasing size, n-1 of them between the final n terms of S(n-1) and the final multiple after the last term of S(n-1). {a(n)} is the limit of this process as n -> inf.
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1
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2, 3, 1, 8, 6, 12, 5, 4, 10, 16, 18, 15, 24, 9, 36, 7, 25, 14, 42, 21, 20, 32, 28, 40, 48, 64, 35, 72, 27, 30, 45, 80, 63, 49, 81, 88, 50, 90, 60, 54, 70, 99, 100, 96, 110, 11, 108, 22, 120, 33, 56, 44, 130, 55, 117, 84, 66, 144, 140, 156, 77, 168, 104, 180, 121, 192, 13
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| After n steps of the construction process n(n-1)/2 terms have been decided.
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EXAMPLE
| 1
2,1,4 (multiples of 2 placed alternately )
2,3,1,6,4,9,(multiples of 3 placed alternately )
2,3,1,8,6,12,4,16,9,20
2,3,1,8,6,12,5,4,10,16,15,9,25,20,30
The next step is to place unused multiples of 6, i.e. 18,24,36,42,48,54 at position marked ##:
2,3,1,8,6,12,5,4,10,16,##,15,##,9,##,25,##,20,##,30,##
...
After the 5-th stage the terms 2,3,1,8,6,12,5,4,10,16 remain unchanged, hence form the initial 10 terms of the desired sequence.
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CROSSREFS
| Sequence in context: A175314 A011152 A078298 * A101281 A106033 A121634
Adjacent sequences: A096060 A096061 A096062 * A096064 A096065 A096066
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KEYWORD
| nonn
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AUTHOR
| Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Jun 18 2004
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EXTENSIONS
| Extended and edited by John W. Layman (layman(AT)math.vt.edu), Jun 06 2005
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