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
Examples
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.
Links
- Dominic McCarty, Table of n, a(n) for n = 1..10000
Crossrefs
Programs
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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
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