cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A302173 Lexicographically first sequence of distinct terms such that any set of three successive digits can be reordered as {d, d+1, d+2}, d being the smallest of the three digits.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 78, 67, 56, 45, 34, 23, 12, 31, 20, 120, 123, 42, 312, 342, 345, 64, 53, 423, 453, 456, 75, 645, 675, 678, 97, 86, 756, 786, 789, 7867, 89, 7897, 867, 564, 534, 231, 201, 234, 567, 897, 8675, 6453, 4231, 2012, 3120, 1201, 2312, 3123, 1231, 2342, 3423, 1234, 2345
Offset: 1

Views

Author

Eric Angelini and Jean-Marc Falcoz, Apr 03 2018

Keywords

Comments

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

Examples

			Terms a(1) to a(10) are obvious;
a(11) is 78 because 78 is the smallest integer not yet in the sequence such that the elements of the sets {8,9,7} and {9,7,8} are three consecutive digits;
a(12) is 67 because 67 is the smallest integer not yet in the sequence such that the elements of the sets {7,8,6} and {8,6,7} are three consecutive digits;
a(13) is 56 because 56 is the smallest integer not yet in the sequence such that the elements of the sets {6,7,5} and {7,5,6} are three consecutive digits;
etc.
		

Crossrefs

Cf. A228326 for the same idea with sets of two digits.

Programs

  • Python
    a, runLength = [i for i in range(10)], 3
    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