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
Keywords
Examples
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 ...
Links
- H. Vic Damnon, Rationals Countability and Cantor's Proof.
Programs
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Mathematica
(* to read the Cantor Matrix *) Table[{n, d}, {n, 13}, {d, 13}] // Grid
Comments