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

1,3

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

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.

Example

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].

Crossrefs

Cf. A336611.

Sequence in context: A029318 A358402 A210381 * A029297 A289871 A257563

Adjacent sequences: A368588 A368589 A368590 * A368592 A368593 A368594

Keyword

base,nonn

Author

Eric Angelini, Dec 31 2023

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

Status

approved