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A320040
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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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0
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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
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OFFSET
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1,4
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COMMENTS
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This is analogous to reading the rows of a triangle in boustrophedon order.
The antidiagonals are in a certain sense palindromic.
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LINKS
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EXAMPLE
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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
...
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MATHEMATICA
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(* to read the Cantor Matrix *) Table[{n, d}, {n, 13}, {d, 13}] // Grid
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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