

A097968


Write each odd 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 A05843 (even numbers): 2 4 6 8 1 0 1 2 1 4 1 6 1 8 2 0 2 2 2 4 2 6 2 8 3 0 3 2 3 4 3 6 3 8... 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.


3



2468101, 21, 41, 61, 82022242628303, 23, 43, 63, 84042444648505, 25, 45, 65, 86062646668707, 27, 47, 67, 88082848688909, 29, 49, 69, 81001021041061081, 101, 1, 211, 411, 611, 81, 201, 221, 241, 261, 281, 301, 3, 213, 413, 613, 81401, 421, 441
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OFFSET

1,1


COMMENTS

This could be roughly rephrased like this: "Rewrite in the most economical way the "even numbers pattern" using only odd numbers, but rearranged. All the numbers of the sequence must be different one from another.


REFERENCES

E. Angelini, "Jeux de suites", in Dossier Pour La Science, pp. 3235, Volume 59 (Jeux math'), April/June 2008, Paris.


LINKS

Table of n, a(n) for n=1..40.


EXAMPLE

We must begin with 2,4,6... and we cannot represent "2" or "24" or "246" by any even label because they just do not exist (available labels carry only odd numbers), so the next possibility is the label "2468101". We couldn't have used "24681" since no label begins with a 0. Labels of L cannot be used more than once.


CROSSREFS

Cf. A098099.
Sequence in context: A144588 A022216 A254988 * A205025 A254774 A254781
Adjacent sequences: A097965 A097966 A097967 * A097969 A097970 A097971


KEYWORD

base,easy,nonn


AUTHOR

Eric Angelini, Sep 22 2004


STATUS

approved



