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Lexicographically earliest sequence of distinct terms such that a(n) shares at least one odd digit with a(n+1).
2

%I #8 Dec 01 2019 23:14:42

%S 1,10,11,12,13,3,23,30,31,14,15,5,25,35,32,33,34,36,37,7,17,16,18,19,

%T 9,29,39,38,43,53,45,50,51,21,41,61,71,27,47,57,52,54,55,56,58,59,49,

%U 69,79,67,70,72,73,63,83,93,89,90,91,81,100,101,102,103,104,105,65,75,74,76,77,78,87

%N Lexicographically earliest sequence of distinct terms such that a(n) shares at least one odd digit with a(n+1).

%C The sequence starts with a(1) = 1 and is always extended with the smallest integer not present that doesn't lead to a contradiction.

%C The sequence is not a permutation of the integers > 0 as no term of A014263 (Numbers that contain even digits only) will ever appear.

%H Jean-Marc Falcoz, <a href="/A303879/b303879.txt">Table of n, a(n) for n = 1..1001</a>

%e a(1) = 1 shares 1 with 10;

%e a(2) = 10 shares 1 with 11;

%e a(3) = 11 shares 1 with 12;

%e a(4) = 12 shares 1 with 13;

%e a(5) = 13 shares 3 with 3;

%e a(6) = 3 shares 3 with 23;

%e a(7) = 23 shares 3 with 30;

%e etc.

%Y Cf. A303880 for the same idea with even digits.

%K nonn,base

%O 1,2

%A _Eric Angelini_ and _Jean-Marc Falcoz_, May 02 2018