

A302499


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.


6



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, 452, 345, 234, 523, 412, 301, 2301, 2341, 2345, 634, 563, 456, 74, 567, 89, 678, 96, 78, 967, 856, 745, 6345, 6745, 6785, 6789, 67856, 785, 67456, 789, 67896, 7856, 7456, 3452, 3412, 3012, 3456, 7896
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OFFSET

1,3


COMMENTS

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.


LINKS

JeanMarc Falcoz, Table of n, a(n) for n = 1..269


EXAMPLE

Terms a(1) to a(10) are obvious;
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;
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;
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;
etc.


CROSSREFS

Cf. A228326 for the same idea with sets of two digits and A302173 for sets of three digits.
Sequence in context: A243023 A243024 A004860 * A024662 A153670 A229184
Adjacent sequences: A302496 A302497 A302498 * A302500 A302501 A302502


KEYWORD

nonn,base


AUTHOR

Eric Angelini and JeanMarc Falcoz, Apr 09 2018


STATUS

approved



