A302499 - OEIS

%I #10 Apr 09 2018 22:56:51

%S 0,1,2,3,4,5,6,7,8,9,67,85,674,56,34,52,341,23,41,230,12,30,123,45,63,

%T 452,345,234,523,412,301,2301,2341,2345,634,563,456,74,567,89,678,96,

%U 78,967,856,745,6345,6745,6785,6789,67856,785,67456,789,67896,7856,7456,3452,3412,3012,3456,7896

%N Lexicographically first sequence of distinct terms such that any set of four successive digits can be reordered as {d, d+1, d+2, d+3}, d being the smallest of the four digits.

%C As the digit 0 has no predecessor and the digit 9 has no successor here, sets of successive digits like {2,1,0,9} and {7,8,9,0} are forbidden.

%H Jean-Marc Falcoz, <a href="/A302499/b302499.txt">Table of n, a(n) for n = 1..269</a>

%e Terms a(1) to a(10) are obvious;

%e a(11) is 67 because 67 is the smallest integer not yet in the sequence such that the elements of the sets {7,8,9,6} and {8,9,6,7} are four consecutive digits;

%e a(12) is 85 because 85 is the smallest integer not yet in the sequence such that the elements of the sets {9,6,7,8} and {6,7,8,5} are four consecutive digits;

%e a(13) is 674 because 674 is the smallest integer not yet in the sequence such that the elements of the three sets {7,8,5,6}, {8,5,6,7} and {5,6,7,4} are four consecutive digits;

%e etc.

%Y Cf. A228326 for the same idea with sets of two digits and A302173 for sets of three digits.

%K nonn,base

%O 1,3

%A _Eric Angelini_ and _Jean-Marc Falcoz_, Apr 09 2018