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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. 0
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 (list; graph; refs; listen; history; text; internal format)
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 A227083 A327571

Adjacent sequences:  A320037 A320038 A320039 * A320041 A320042 A320043

KEYWORD

nonn

AUTHOR

Robert G. Wilson v, Oct 03 2018

STATUS

approved

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Last modified January 29 16:58 EST 2020. Contains 331347 sequences. (Running on oeis4.)