A302503 Lexicographically first sequence of distinct terms such that any set of eight successive digits can be reordered as {d, d+1, d+2, d+3, d+4, d+5, d+6, d+7}, d being the smallest of the eight digits

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 23, 45, 67, 81, 234, 56, 70, 12, 34, 567, 89, 2345, 678, 92, 345, 6781, 23456, 78, 123, 456, 701, 234567, 812, 3456, 781, 2345670, 1234, 5670, 12345, 670, 123456, 789, 2345678, 923, 4567, 892, 34567, 8123, 45670, 1234567, 8923, 45678, 9234, 5678, 92345, 6789, 23456781, 23456701

Offset

1,3

Comments

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

Links

Table of n, a(n) for n=1..58.

Example

Terms a(1) to a(10) are obvious;
a(11) is 23 because 23 is the smallest integer not yet in the sequence such that the elements of the sets {3,4,5,6,7,8,9,2} and {4,5,6,7,8,9,2,3} are eight consecutive digits;
a(12) is 45 because 45 is the smallest integer not yet in the sequence such that the elements of the sets {5,6,7,8,9,2,3,4} and {6,7,8,9,2,3,4,5} are eight consecutive digits;
a(13) is 67 because 67 is the smallest integer not yet in the sequence such that the elements of the sets {7,8,9,2,3,4,5,6} and {8,9,2,3,4,5,6,7} are eight 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), A302500 (sets of five digits), A302501 (sets of six digits) and A302502 (sets of seven digits).

Sequence in context: A307636 A373722 A048386 * A198044 A133134 A133505

Adjacent sequences: A302500 A302501 A302502 * A302504 A302505 A302506

Keyword

nonn,base

Author

Eric Angelini and Jean-Marc Falcoz, Apr 09 2018

Status

approved