A302504 Lexicographically first sequence of distinct terms such that any set of nine successive digits can be reordered as {d, d+1, d+2, d+3, d+4, d+5, d+6, d+7, d+8}, d being the smallest of the nine digits.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 34, 56, 78, 91, 23, 45, 67, 80, 123, 456, 780, 1234, 567, 89, 12345, 678, 912, 345, 6780, 123456, 789, 1234567, 801, 234, 5678, 9123, 4567, 891, 2345, 6789, 12345678, 91234, 56780, 123456780, 123456789

Offset

1,3

Comments

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

Links

Dominic McCarty, Table of n, a(n) for n = 1..10000

Example

Terms a(1) to a(10) are obvious;
a(11) is 12 because 12 is the smallest integer not yet in the sequence such that the elements of the sets {2,3,4,5,6,7,8,9,1} and {3,4,5,6,7,8,9,1,2} are nine consecutive digits;
a(12) is 34 because 34 is the smallest integer not yet in the sequence such that the elements of the sets {4,5,6,7,8,9,1,2,3} and {5,6,7,8,9,1,2,3,4} are nine consecutive digits;
a(13) is 56 because 56 is the smallest integer not yet in the sequence such that the elements of the sets {6,7,8,9,1,2,3,4,5} and {7,8,9,1,2,3,4,5,6} are nine consecutive digits;
etc.

Prog

(Python)
a, runLength = [i for i in range(10)], 9
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 02 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), A302502 (sets of seven digits) and A302503 (sets of eight digits).

Sequence in context: A289791 A290386 A290388 * A165307 A081549 A085889

Adjacent sequences: A302501 A302502 A302503 * A302505 A302506 A302507

Keyword

nonn,base,look

Author

Eric Angelini and Jean-Marc Falcoz, Apr 09 2018

Status

approved