A368591 The sequence is both a succession of triples of monotonically increasing numbers and a succession of triples of monotonically increasing digits. This is the lexicographically earliest such sequence starting with a(1) = 0 formed by distinct number-triples.

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

Offset: 1

Author

Eric Angelini, Dec 31 2023

Keywords

• base
• nonn

Comments

When will 2024 appear?

Terms up to n=507:

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

Examples

			The first 10 distinct triples of monotonically increasing numbers are: [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].
The first 10 distinct triples of monotonically increasing numbers using altogether more than 3 digits are: [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].
The above 10 triples are also a succession of triples of monotonically increasing digits: [0,1,2][0,1,2],[12,3],[12,3][0,1,2],[13,4],[12,3],[0,1,2],[14,5],[12,3][0,1,2],[15,6],[12,3][0,1,2].
		

Links

• Eric Angelini, Table of n, a(n) for n = 1..507
• Eric Angelini, Triples for the new year, Personal blog, December 31, 2023.
• Eric Angelini, Triples for the new year, local copy of blog post.

Crossrefs

Cf. A336611.

Extensions

More than the usual number of terms are shown (with permission of the editors) in order to reach the interesting terms.

Terms moved to comment to avoid excessive length of DATA by Hugo Pfoertner, Jan 02 2025