

A098099


Consider the succession of single digits of the positive odd integers: 1 3 5 7 9 1 1 1 3 1 5 1 7 1 9 2 1 2 3 2 5 ... (A031312). This sequence is the lexicographically earliest sequence of distinct positive even integers that produces the same succession of digits.


4



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
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OFFSET

1,1


COMMENTS

Original name: "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."
This could be roughly rephrased like this: Rewrite in the most economical way the "odd numbers pattern" using only even 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

Michael De Vlieger, Table of n, a(n) for n = 1..10000


EXAMPLE

We must begin with "1,3,5..." and we cannot use "1" or "13" or "135" (only even terms are available), so the first possibility is "1357911131517192". For "199,201,203..." we won't be allowed to use "1992", for instance, since no term begins with a 0.


MATHEMATICA

f[lst_List, k_] := Block[{L = lst, g, w, a = {}, m}, g[x_] := First@ FirstPosition[x, i_ /; EvenQ@ i]; Do[w = Take[L, g@ L]; L = Drop[L, Length@ w]; m = Take[L, g@ L]; While[Or[MemberQ[a, FromDigits@ w], IntegerLength@ FromDigits@ m < Length@ m], w = Join[w, m]; L = Drop[L, Length@ m]; m = Take[L, g@ L]]; AppendTo[a, FromDigits@ w], {k}]; a]; f[Flatten@ Map[IntegerDigits, Range[1, 1000, 2]], 35] (* Michael De Vlieger, Nov 28 2015, Version 10 *)


CROSSREFS

Cf. A005408, A005843, A097487, A097968.
Sequence in context: A134692 A288286 A217683 * A338442 A257138 A288279
Adjacent sequences: A098096 A098097 A098098 * A098100 A098101 A098102


KEYWORD

base,easy,nonn


AUTHOR

Eric Angelini, Sep 22 2004


EXTENSIONS

Name and Example edited by Danny Rorabaugh, Nov 28 2015


STATUS

approved



