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URL: https://oeis.org/A302499

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A302499
Lexicographically first sequence of distinct terms such that any set of four successive digits can be reordered as {d, d+1, d+2, d+3}, d being the smallest of the four digits.
6
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 67, 85, 674, 56, 34, 52, 341, 23, 41, 230, 12, 30, 123, 45, 63, 452, 345, 234, 523, 412, 301, 2301, 2341, 2345, 634, 563, 456, 74, 567, 89, 678, 96, 78, 967, 856, 745, 6345, 6745, 6785, 6789, 67856, 785, 67456, 789, 67896, 7856, 7456, 3452, 3412, 3012, 3456, 7896
OFFSET
1,3
COMMENTS
As the digit 0 has no predecessor and the digit 9 has no successor here, sets of successive digits like {2,1,0,9} and {7,8,9,0} are forbidden.
LINKS
Dominic McCarty, Table of n, a(n) for n = 1..10000 (first 269 terms from Jean-Marc Falcoz)
EXAMPLE
Terms a(1) to a(10) are obvious;
a(11) is 67 because 67 is the smallest integer not yet in the sequence such that the elements of the sets {7,8,9,6} and {8,9,6,7} are four consecutive digits;
a(12) is 85 because 85 is the smallest integer not yet in the sequence such that the elements of the sets {9,6,7,8} and {6,7,8,5} are four consecutive digits;
a(13) is 674 because 674 is the smallest integer not yet in the sequence such that the elements of the three sets {7,8,5,6}, {8,5,6,7} and {5,6,7,4} are four consecutive digits;
etc.
PROG
(Python)
a, runLength = [i for i in range(10)], 4
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 and A302173 for sets of three digits.
Sequence in context: A243023 A243024 A004860 * A024662 A153670 A229184
KEYWORD
nonn,base
AUTHOR
STATUS
approved