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Search: id:A098099
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| A098099 |
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Write each even integer >0 on a single label. Put the labels in numerical order to form an infinite sequence L. Now consider the succession of single digits of A005408 (odd numbers): 1 3 5 7 9 1 1 1 3 1 5 1 7 1 9 2 1 2 3 2 5 2 7 2 9 3 1 3 3 3 5 3 7 3 9... The sequence S gives a rearrangement of the labels that reproduces the same succession of digits, subject to the constraint that the smallest label must be used that does not lead to a contradiction. |
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+0
4
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| 1357911131517192, 12, 32, 52, 72, 931333537394, 14, 34, 54, 74, 951535557596, 16, 36, 56, 76, 971737577798, 18, 38, 58, 78, 9919395979910, 110, 310, 510, 710, 911111311511711912, 112, 312, 512, 712, 913113313513713914, 114, 314, 514, 714
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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This could be roughly rephrased like this: "Re-write in the most economical way the "odd numbers pattern" using only even numbers, but re-arranged. All the numbers of the sequence must be different one from another.
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REFERENCES
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E. Angelini, "Jeux de suites", in Dossier Pour La Science, pp. 32-35, Volume 59 (Jeux math'), April/June 2008, Paris.
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EXAMPLE
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We must begin with 1,3,5..., and we cannot represent "1" or "13" or "135" by any even label because they just do not exist (available labels carry only odd numbers), so the next possibility is the label "1357911131517192". For "199,201,203..." we won't be allowed to use "1992", for instance, since no label begins with a 0. Labels of L cannot be used more than once.
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CROSSREFS
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Cf. A097968, A097487.
Sequence in context: A095431 A072719 A134692 this_sequence A067495 A047698 A058445
Adjacent sequences: A098096 A098097 A098098 this_sequence A098100 A098101 A098102
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KEYWORD
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base,easy,nonn
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AUTHOR
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Eric Angelini (eric.angelini(AT)kntv.be), Sep 22 2004
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