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⇱ A302503 - OEIS

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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.
2
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
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.
PROG
(Python)
a, runLength = [i for i in range(10)], 8
def helper(s, k, l, a):
if k not in a: return k
return min([helper(s[(2-l):]+str(i), int(str(k)+str(i)), l, a) for i in range(10) if (k!=0 or i!=0) and s.find(str(i))==-1 and (all(d[n]+1==d[n+1] for n in range(l-1)) if (d:=sorted([int((s+str(i))[n]) for n in range(l)])) else False)])
while len(a)<100: a.append(helper(("".join(map(str, a)))[(1-runLength):], 0, runLength, a))
print(a) # Dominic McCarty, Feb 03 2025
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
KEYWORD
nonn,base
AUTHOR
STATUS
approved