A320040 Consider the Cantor matrix of rational numbers. This sequence reads the numerator, then the denominator as one moves through the matrix along alternate up and down antidiagonals.

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

Offset

1,4

Comments

This is analogous to reading the rows of a triangle in boustrophedon order.

The antidiagonals are in a certain sense palindromic.

Links

Table of n, a(n) for n=1..90.

H. Vic Damnon, Rationals Countability and Cantor's Proof.

Example

The Cantor Matrix begins:
=========================================================================
n\d|   1    2    3    4    5    6    7    8    9    10    11    12    13
---|---------------------------------------------------------------------
1  |  1/1  1/2  1/3  1/4  1/5  1/6  1/7  1/8  1/9  1/10  1/11  1/12  1/13
2  |  2/1  2/2  2/3  2/4  2/5  2/6  2/7  2/8  2/9  2/10  2/11  2/12  2/13
3  |  3/1  3/2  3/3  3/4  3/5  3/6  3/7  3/8  3/9  3/10  3/11  3/12  3/13
4  |  4/1  4/2  4/3  4/4  4/5  4/6  4/7  4/8  4/9  4/10  4/11  4/12  4/13
5  |  5/1  5/2  5/3  5/4  5/5  5/6  5/7  5/8  5/9  5/10  5/11  5/12  5/13
6  |  6/1  6/2  6/3  6/4  6/5  6/6  6/7  6/8  6/9  6/10  6/11  6/12  6/13
7  |  7/1  7/2  7/3  7/4  7/5  7/6  7/7  7/8  7/9  7/10  7/11  7/12  7/13
8  |  8/1  8/2  8/3  8/4  8/5  8/6  8/7  8/8  8/9  8/10  8/11  8/12  8/13
9  |  9/1  9/2  9/3  9/4  9/5  9/6  9/7  9/8  9/9  9/10  9/11  9/12  9/13
10 | 10/1 10/2 10/3 10/4 10/5 10/6 10/7 10/8 10/9 10/10 10/11 10/12 10/13
11 | 11/1 11/2 11/3 11/4 11/5 11/6 11/7 11/8 11/9 11/10 11/11 11/12 11/13
12 | 12/1 12/2 12/3 12/4 12/5 12/6 12/7 12/8 12/9 12/10 12/11 12/12 12/13
13 | 13/1 13/2 13/3 13/4 13/5 13/6 13/7 13/8 13/9 13/10 13/11 13/12 13/13
...

Mathematica

(* to read the Cantor Matrix *) Table[{n, d}, {n, 13}, {d, 13}] // Grid

Crossrefs

Cf. A020652, A020653.

Sequence in context: A238882 A279287 A135352 * A072528 A368060 A227083

Adjacent sequences: A320037 A320038 A320039 * A320041 A320042 A320043

Keyword

nonn

Author

Robert G. Wilson v, Oct 03 2018

Status

approved