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

%I #7 Apr 09 2018 22:57:00

%S 0,1,2,3,4,5,6,7,8,9,56,78,45,67,34,562,345,12,340,123,40,1234,51,23,

%T 401,234,512,3401,2340,12340,12345,62,3451,2345,623,451,23401,23451,

%U 23456,73,456,734,567,84,5673,4562,3456,784,5678,95,678,956,789,56784,56734,5623,4512,34012,34512,34562,34567,89

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

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

%H Jean-Marc Falcoz, <a href="/A302500/b302500.txt">Table of n, a(n) for n = 1..257</a>

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

%e a(11) is 56 because 56 is the smallest integer not yet in the sequence such that the elements of the sets {6,7,8,9,5} and {7,8,9,5,6} are five consecutive digits;

%e a(12) is 78 because 78 is the smallest integer not yet in the sequence such that the elements of the sets {8,9,5,6,7} and {9,5,6,7,8} are five consecutive digits;

%e a(13) is 45 because 45 is the smallest integer not yet in the sequence such that the elements of the sets {5,6,7,8,4} and {6,7,8,4,5} are five consecutive digits;

%e etc.

%Y Cf. A228326 for the same idea with sets of two digits, A302173 for sets of three digits and A302499 for sets of four digits.

%K nonn,base

%O 1,3

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