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URL: https://oeis.org/A302501

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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.
4
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
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.
PROG
(Python)
a, runLength = [i for i in range(10)], 6
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) and A302500 (sets of five digits).
Sequence in context: A342755 A129513 A281745 * A183532 A257829 A219327
KEYWORD
nonn,base
AUTHOR
STATUS
approved