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A302502
Lexicographically first sequence of distinct terms such that any set of seven successive digits can be reordered as {d, d+1, d+2, d+3, d+4, d+5, d+6}, d being the smallest of the seven digits.
2
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 34, 56, 78, 23, 45, 67, 12, 345, 60, 123, 456, 71, 234, 560, 1234, 567, 82, 3456, 712, 34560, 12345, 601, 2345, 671, 23456, 782, 34567, 89, 345678, 93, 4567, 823, 45671, 234560, 123456, 789, 3456782, 345671, 234567, 893, 45678, 934, 5678, 9345, 678, 93456, 7823, 456712, 345601
OFFSET
1,3
COMMENTS
As the digit 0 has no predecessor and the digit 9 has no successor here, sets of successive digits like {5,4,3,2,1,0,9} and {4,5,6,7,8,9,0} are forbidden.
EXAMPLE
Terms a(1) to a(10) are obvious;
a(11) is 34 because 34 is the smallest integer not yet in the sequence such that the elements of the sets {4,5,6,7,8,9,3} and {5,6,7,8,9,3,4} are seven consecutive digits;
a(12) is 56 because 56 is the smallest integer not yet in the sequence such that the elements of the sets {6,7,8,9,3,4,5} and {7,8,9,3,4,5,6} are seven consecutive digits;
a(13) is 78 because 78 is the smallest integer not yet in the sequence such that the elements of the sets {8,9,3,4,5,6,7} and {9,3,4,5,6,7,8} are seven 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) and A302501 (sets of six digits).
Sequence in context: A271534 A072482 A254958 * A257830 A343050 A276143
KEYWORD
nonn,base
AUTHOR
STATUS
approved