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A302503
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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
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1
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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
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OFFSET
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1,3
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COMMENTS
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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.
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LINKS
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EXAMPLE
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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.
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CROSSREFS
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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).
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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