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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.

%I A302499 #14 Feb 03 2025 21:24:04
%S A302499 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,
%T A302499 452,345,234,523,412,301,2301,2341,2345,634,563,456,74,567,89,678,96,
%U A302499 78,967,856,745,6345,6745,6785,6789,67856,785,67456,789,67896,7856,7456,3452,3412,3012,3456,7896
%N 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.
%C A302499 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.
%H A302499 Dominic McCarty, <a href="/A302499/b302499.txt">Table of n, a(n) for n = 1..10000</a> (first 269 terms from Jean-Marc Falcoz)
%e A302499 Terms a(1) to a(10) are obvious;
%e A302499 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;
%e A302499 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;
%e A302499 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;
%e A302499 etc.
%o A302499 (Python)
%o A302499 a, runLength = [i for i in range(10)], 4
%o A302499 def helper(s, k, l, a):
%o A302499     if k not in a: return k
%o A302499     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)])
%o A302499 while len(a)<100: a.append(helper(("".join(map(str, a)))[(1-runLength):], 0, runLength, a))
%o A302499 print(a) # _Dominic McCarty_, Feb 03 2025
%Y A302499 Cf. A228326 for the same idea with sets of two digits and A302173 for sets of three digits.
%K A302499 nonn,base
%O A302499 1,3
%A A302499 _Eric Angelini_ and _Jean-Marc Falcoz_, Apr 09 2018