

A097968


Consider the succession of single digits of the positive even integers: 2 4 6 8 1 0 1 2 1 4 1 6 1 8 2 0 2 2 2 4 ... (A036211). This sequence is the lexicographically earliest sequence of distinct positive odd integers that produces the same succession of digits.


4



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

Original name: "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 A005843 (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."
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.


LINKS

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


EXAMPLE

We must begin with "2,4,6..." and we cannot use "2" or "24" or "246" (only odd terms are available), so the first possibility is "2468101". We could not have used "24681" 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_ /; OddQ@ 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, 2 Range@ 80], 40] (* Michael De Vlieger, Nov 28 2015, Version 10 *)


CROSSREFS



KEYWORD

base,easy,nonn


AUTHOR



EXTENSIONS



STATUS

approved



