A302504 - OEIS

%I #6 Apr 23 2022 16:29:14

%S 0,1,2,3,4,5,6,7,8,9,12,34,56,78,91,23,45,67,80,123,456,780,1234,567,

%T 89,12345,678,912,345,6780,123456,789,1234567,801,234,5678,9123,4567,

%U 891,2345,6789,12345678,91234,56780,123456780,123456789

%N Lexicographically first sequence of distinct terms such that any set of nine successive digits can be reordered as {d, d+1, d+2, d+3, d+4, d+5, d+6, d+7, d+8}, d being the smallest of the nine digits.

%C As the digit 0 has no predecessor and the digit 9 has no successor here, sets of successive digits like {7,6,5,4,3,2,1,0,9} and {2,3,4,5,6,7,8,9,0} are forbidden.

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

%e a(11) is 12 because 12 is the smallest integer not yet in the sequence such that the elements of the sets {2,3,4,5,6,7,8,9,1} and {3,4,5,6,7,8,9,1,2} are nine consecutive digits;

%e a(12) is 34 because 34 is the smallest integer not yet in the sequence such that the elements of the sets {4,5,6,7,8,9,1,2,3} and {5,6,7,8,9,1,2,3,4} are nine consecutive digits;

%e a(13) is 56 because 56 is the smallest integer not yet in the sequence such that the elements of the sets {6,7,8,9,1,2,3,4,5} and {7,8,9,1,2,3,4,5,6} are nine consecutive digits;

%e etc.

%Y Cf. A228326 for the same idea with sets of two digits, A302173 (sets of three digits), A302499 (sets of four digits), A302500 (sets of five digits), A302501 (sets of six digits), A302502 (sets of seven digits) and A302503 (sets of eight digits).

%K nonn,base,more

%O 1,3

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