%I
%S 2,12,20,10,30,40,4,14,24,21,22,23,25,26,6,16,36,46,34,41,42,27,28,8,
%T 18,38,48,43,44,45,47,49,54,64,56,60,50,70,80,58,68,61,62,29,32,52,72,
%U 82,78,81,83,84,74,94,104,90,100,101,102,92,112,120,103,105,106,63,65,66,67,69,76
%N Lexicographically earliest sequence of distinct terms such that a(n) shares at least one even digit with a(n+1).
%C The sequence starts with a(1) = 2 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 A014261 (Numbers that contain odd digits only) will ever show.
%H JeanMarc Falcoz, <a href="/A303880/b303880.txt">Table of n, a(n) for n = 1..1001</a>
%e a(1) = 2 shares 2 with 12;
%e a(2) = 12 shares 2 with 20;
%e a(3) = 20 shares 0 with 10;
%e a(4) = 10 shares 0 with 30;
%e a(5) = 30 shares 0 with 40;
%e a(6) = 40 shares 4 with 4;
%e a(7) = 4 shares 4 with 14;
%e a(8) = 14 shares 4 with 24;
%e etc.
%Y Cf. A303879 for the same idea with odd digits.
%K nonn,base,changed
%O 1,1
%A _Eric Angelini_ and _JeanMarc Falcoz_, May 02 2018
