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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.
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%I #23 Nov 09 2018 20:46:48

%S 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,

%T 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,

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

%N 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.

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

%C The antidiagonals are in a certain sense palindromic.

%H H. Vic Damnon, <a href="http://www.gauge-institute.org/zigzag/cantorzigzagP.pdf">Rationals Countability and Cantor's Proof.</a>

%e The Cantor Matrix begins:

%e =========================================================================

%e n\d| 1 2 3 4 5 6 7 8 9 10 11 12 13

%e ---|---------------------------------------------------------------------

%e 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

%e 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

%e 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

%e 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

%e 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

%e 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

%e 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

%e 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

%e 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

%e 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

%e 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

%e 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

%e 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

%e ...

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

%Y Cf. A020652, A020653.

%K nonn

%O 1,4

%A _Robert G. Wilson v_, Oct 03 2018