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A097488
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Write each multiple of 3 on a single label. Put the labels in numerical order to form an infinite sequence L. Now consider the succession of single digits of A008585 (multiples of 3): 3 6 9 1 2 1 5 1 8 2 1 2 4 2 7 3 0 3 3 3 6 3 9 4 2 4 5 4 8... The sequence S gives a rearrangement of the labels that reproduces the same succession of digits, subject to the constraints that a label of L cannot represent itself and the smallest label must be used that does not lead to a contradiction.
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1
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36, 9, 12, 15, 18, 21, 24, 27, 30, 3, 336, 39, 42, 45, 48, 51, 54, 57, 60, 6, 36, 669, 72, 75, 79, 81, 84, 87, 90, 93, 96, 99, 102, 105, 108, 111, 114, 117, 120, 123, 126, 129, 132, 135, 138, 141, 144, 147, 150, 153, 156, 159, 162, 165
(list; graph; refs; listen; history; internal format)
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OFFSET
| 3,1
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COMMENTS
| This could be roughly rephrased like this: "Re-write in the most economical way the "multiples-of-3 pattern" using only multiples of 3, but re-arranged. All the numbers of the sequence must be different one from another."
This could be roughly rephrased like this: "Re-write in the most economical way the "multiples-of-3 pattern" using only multiples of 3, but re-arranged. All terms of the sequence must be different one from another." [From Eric Angelini (eric.angelini(AT)skynet.be), Aug 12 2008]
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EXAMPLE
| We must begin with 3,6,9,... and we cannot represent "3" by the label 3", so the next possibility is the label "36". After "2124" we must get "27 30 33..." and we cannot use "273" since no label begins with a 0. So the next term is "2730". Labels of L cannot be used more than once.
We must begin with 3,6,9,12,... and we cannot represent "3" by the label "3", so the next possibility is the label "36". The next term must be the smallest available label not leading to a contradiction, thus "9". The next one will be "12", etc. After the label "30" the smallest available label is "3". After this "3" we cannot use the label "33" as this "33" would represent itself -- we thus take the smallest available label which is "336". No label is allowed to start with a leading zero. [From Eric Angelini (eric.angelini(AT)skynet.be), Aug 12 2008]
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CROSSREFS
| Sequence in context: A100252 A020340 A181759 * A061046 A109256 A066583
Adjacent sequences: A097485 A097486 A097487 * A097489 A097490 A097491
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KEYWORD
| base,easy,nonn
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AUTHOR
| Eric Angelini (eric.angelini(AT)kntv.be), Sep 19 2004
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EXTENSIONS
| Corrected and extended by Jacques ALARDET and Eric Angelini (eric.angelini(AT)skynet.be), Aug 12 2008
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