A302501 Lexicographically first sequence of distinct terms such that any set of six successive digits can be reordered as {d, d+1, d+2, d+3, d+4, d+5}, d being the smallest of the six digits.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 45, 67, 83, 456, 72, 34, 56, 12, 345, 61, 23, 450, 123, 4501, 234, 50, 1234, 501, 2345, 612, 3450, 12345, 672, 3456, 78, 94, 567, 89, 4567, 834, 5672, 34561, 23450, 123450, 123456, 723, 4561, 23456, 783, 45672, 34567, 894, 5678, 945, 678, 9456, 789, 45678, 94567, 8345, 6723, 45612, 34501, 234501, 234561, 234567, 8945, 6783, 456723, 456123, 45012, 345012

Offset

1,3

Comments

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

Links

Table of n, a(n) for n=1..72.

Example

Terms a(1) to a(10) are obvious;
a(11) is 45 because 45 is the smallest integer not yet in the sequence such that the elements of the sets {5,6,7,8,9,4} and {6,7,8,9,4,5} are six consecutive digits;
a(12) is 67 because 67 is the smallest integer not yet in the sequence such that the elements of the sets {7,8,9,4,5,6} and {8,9,4,5,6,7} are six consecutive digits;
a(13) is 83 because 83 is the smallest integer not yet in the sequence such that the elements of the sets {9,4,5,6,7,8} and {4,5,6,7,8,3} are six consecutive digits;
etc.

Crossrefs

Cf. A228326 for the same idea with sets of two digits, A302173 (sets of three digits), A302499 (sets of four digits) and A302500 (sets of five digits).

Sequence in context: A342755 A129513 A281745 * A183532 A257829 A219327

Adjacent sequences: A302498 A302499 A302500 * A302502 A302503 A302504

Keyword

nonn,base

Author

Eric Angelini and Jean-Marc Falcoz, Apr 09 2018

Status

approved