Triples for the new year


(Dall-e creation)

The hereunder sequence S is both a succession of triples of monotonically increasing numbers and a succession of triples of monotonically increasing digits.
S is the lexicographically earliest such sequence with distinct number-triples:

S = 0,1,2,0,1,3,0,1,4,0,1,5,0,1,6,0,1,7,0,1,8,0,1,9,0,2,3,0,2,4,0,2,5,0,2,6,0,2,7,0,2,8,0,2,9,0,3,4,0,3,5,0,3,6,0,3,7,0,3,8,0,3,9,0,4,5,0,4,6,0,4,7,0,4,8,0,4,9,0,5,6,0,5,7,0,5,8,0,5,9,0,6,7,0,6,8,0,6,9,0,7,8,0,7,9,0,8,9,1,2,3,1,2,4,1,2,5,1,2,6,1,2,7,1,2,8,1,2,9,1,3,4,1,3,5,1,3,6,1,3,7,1,3,8,1,3,9,1,4,5,1,4,6,1,4,7,1,4,8,1,4,9,1,5,6,1,5,7,1,5,8,1,5,9,1,6,7,1,6,8,1,6,9,1,7,8,1,7,9,1,8,9,2,3,4,2,3,5,2,3,6,2,3,7,2,3,8,2,3,9,2,4,5,2,4,6,2,4,7,2,4,8,2,4,9,2,5,6,2,5,7,2,5,8,2,5,9,2,6,7,2,6,8,2,6,9,2,7,8,2,7,9,2,8,9,3,4,5,3,4,6,3,4,7,3,4,8,3,4,9,3,5,6,3,5,7,3,5,8,3,5,9,3,6,7,3,6,8,3,6,9,3,7,8,3,7,9,3,8,9,4,5,6,4,5,7,4,5,8,4,5,9,4,6,7,4,6,8,4,6,9,4,7,8,4,7,9,4,8,9,5,6,7,5,6,8,5,6,9,5,7,8,5,7,9,5,8,9,6,7,8,6,7,9,6,8,9,7,8,9,0,1,20,1,2,12,3,12,30,1,2,13,4,12,30,1,2,14,5,12,30,1,2,15,6,12,30,1,2,16,7,12,30,1,2,17,8,12,30,1,2,18,9,12,30,1,2,23,4,12,31,2,3,12,3,12,31,2,3,13,4,12,31,2,3,14,5,12,31,2,3,15,6,12,31,2,3,16,7,12,31,2,3,17,8,12,31,2,3,18,9,12,31,2,3,23,4,12,32,3,4,12,3,12,32,3,4,13,4,12,32,3,4,14,5,12,32,3,4,15,6,12,32,3,4,16,7,12,32,3,4,17,8,12,32,3,4,18,9,12,32,3,4,23,4,12,33,...

Here is how S was constructed.
First (alternating yellow and white colors for readability), we have the 120 triples which are both numbers and digits in monotonically increasing order:

S =
0,1,2,0,1,3,0,1,4,0,1,5,0,1,6,0,1,7,0,1,8,0,1,9,
0,2,3,0,2,4,0,2,5,0,2,6,0,2,7,0,2,8,0,2,9,
0,3,4,0,3,5,0,3,6,0,3,7,0,3,8,0,3,9,
0,4,5,0,4,6,0,4,7,0,4,8,0,4,9,
0,5,6,0,5,7,0,5,8,0,5,9,
0,6,7,0,6,8,0,6,9,
0,7,8,0,7,9,
0,8,9,

1,2,3,1,2,4,1,2,5,1,2,6,1,2,7,1,2,8,1,2,9,
1,3,4,1,3,5,1,3,6,1,3,7,1,3,8,1,3,9,
1,4,5,1,4,6,1,4,7,1,4,8,1,4,9,
1,5,6,1,5,7,1,5,8,1,5,9,
1,6,7,1,6,8,1,6,9,
1,7,8,1,7,9,
1,8,9,

2,3,4,2,3,5,2,3,6,2,3,7,2,3,8,2,3,9,
2,4,5,2,4,6,2,4,7,2,4,8,2,4,9,
2,5,6,2,5,7,2,5,8,2,5,9,
2,6,7,2,6,8,2,6,9,
2,7,8,2,7,9,
2,8,9,

3,4,5,3,4,6,3,4,7,3,4,8,3,4,9,
3,5,6,3,5,7,3,5,8,3,5,9,
3,6,7,3,6,8,3,6,9,
3,7,8,3,7,9,
3,8,9,

4,5,6,4,5,7,4,5,8,4,5,9,
4,6,7,4,6,8,4,6,9,
4,7,8,4,7,9,
4,8,9,

5,6,7,5,6,8,5,6,9,
5,7,8,5,7,9,
5,8,9,

6,7,8,6,7,9,
6,8,9,

7,8,9,

Next are the number-triples having 3 numbers in monotonically increasing order and using altogether more than 3 digits (grey and white colors):

0,1,20,

1,2,12,3,12,30,1,2,13,4,12,30,1,2,14,5,12,30,1,2,15,6,12,30,1,2,16,7,12,30,1,2,17,8,12,30,1,2,18,9,12,30,1,2,23,4,12,31,

2,3,12,3,12,31,2,3,13,4,12,31,2,3,14,5,12,31,2,3,15,6,12,31,2,3,16,7,12,31,2,3,17,8,12,31,2,3,18,9,12,31,2,3,23,4,12,32,

3,4,12,3,12,32,3,4,13,4,12,32,3,4,14,5,12,32,3,4,15,6,12,32,3,4,16,7,12,32,3,4,17,8,12,32,3,4,18,9,12,32,3,4,23,4,12,33,...

The above grey/white succession of number-triples is also a succession of digit-triples (digits in monotonically increasing order, aqua/white color):

0,1,20,

1,2,12,3,12,30,1,2,13,4,12,30,1,2,14,5,12,30,1,2,15,6,12,30,1,2,16,7 ,12,30,1,2,17,8,12,30,1,2,18,9,12,30,1,2,23,4,12,31,

2,3,12,3,12,31,2,3,13,4,12,31,2,3,14,5,12,31,2,3,15,6,12,31,2,3,16,7,12,31,2,3,17,8,12,31,2,3,18,9,12,31,2,3,23,4,12,32,

3,4,12,3,12,32,3,4,13,4,12,32,3,4,14,5,12,32,3,4,15,6,12,32,3,4,16,7,12,32,3,4,17,8,12,32,3,4,18,9,12,32,3,4,23,4,12,33,...

The successive yellow/white triples and grey/white triples form S:

S = 0,1,2,0,1,3,0,1,4,0,1,5,0,1,6,0,1,7,0,1,8,0,1,9,0,2,3,0,2,4,0,2,5,0,2,6,0,2,7,0,2,8,0,2,9,0,3,4,0,3,5,0,3,6,0,3,7,0,3,8,0,3,9,0,4,5,0,4,6,0,4,7,0,4,8,0,4,9,0,5,6,0,5,7,0,5,8,0,5,9,0,6,7,0,6,8,0,6,9,0,7,8,0,7,9,0,8,9,1,2,3,1,2,4,1,2,5,1,2,6,1,2,7,1,2,8,1,2,9,1,3,4,1,3,5,1,3,6,1,3,7,1,3,8,1,3,9,1,4,5,1,4,6,1,4,7,1,4,8,1,4,9,1,5,6,1,5,7,1,5,8,1,5,9,1,6,7,1,6,8,1,6,9,1,7,8,1,7,9,1,8,9,2,3,4,2,3,5,2,3,6,2,3,7,2,3,8,2,3,9,2,4,5,2,4,6,2,4,7,2,4,8,2,4,9,2,5,6,2,5,7,2,5,8,2,5,9,2,6,7,2,6,8,2,6,9,2,7,8,2,7,9,2,8,9,3,4,5,3,4,6,3,4,7,3,4,8,3,4,9,3,5,6,3,5,7,3,5,8,3,5,9,3,6,7,3,6,8,3,6,9,3,7,8,3,7,9,3,8,9,4,5,6,4,5,7,4,5,8,4,5,9,4,6,7,4,6,8,4,6,9,4,7,8,4,7,9,4,8,9,5,6,7,5,6,8,5,6,9,5,7,8,5,7,9,5,8,9,6,7,8,6,7,9,6,8,9,7,8,9,0,1,20,1,2,12,3,12,30,1,2,13,4,12,30,1,2,14,5,12,30,1,2,15,6,12,30,1,2,16,7,12,30,1,2,17,8,12,30,1,2,18,9,12,30,1,2,23,4,12,31,2,3,12,3,12,31,2,3,13,4,12,31,2,3,14,5,12,31,2,3,15,6,12,31,2,3,16,7,12,31,2,3,17,8,12,31,2,3,18,9,12,31,2,3,23,4,12,32,3,4,12,3,12,32,3,4,13,4,12,32,3,4,14,5,12,32,3,4,15,6,12,32,3,4,16,7,12,32,3,4,17,8,12,32,3,4,18,9,12,32,3,4,23,4,12,33,...

Question
When will 2024 appear in S?
Happy New Year to all – and thanks again to the 2023 contributors!
(this seq will enter the OEIS soon, I hope)
(Dall-e creation)




Commentaires

  1. JamesMcMahon2 janvier 2024 à 17:04

    I see A368591 is proposed. You have my vote for approval (but I'm not an editor). Happy and prosperous 2024!

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