A344009 The Tchoukaillon array of order infinity read by downward antidiagonals.

1, 2, 3, 4, 5, 7, 6, 8, 9, 13, 10, 11, 14, 15, 19, 12, 16, 17, 21, 25, 27, 18, 20, 23, 26, 29, 31, 39, 22, 24, 28, 33, 37, 41, 43, 49, 30, 32, 35, 38, 44, 45, 51, 61, 63, 34, 36, 40, 47, 50, 55, 62, 65, 67, 79, 42, 46, 52, 53, 57, 64, 69, 73, 85, 87, 91, 48, 54, 56, 66, 68, 74, 75, 86, 89, 99, 103, 109

Offset: 1

Author

N. J. A. Sloane, Jun 09 2021, based on an email from Don Knuth, Jun 08 2021

Keywords

• nonn
• tabl

Examples

			The array begins:
1, 2, 4, 6, 10, 12, 18, 22, 30, 34, 42, 48, 58, 60, 78, 82, 102, 108, 118, 132, 150, 154, 174, 192, 210, 214, 240, 258, 274, 282, 322, 330, ...
3, 5, 8, 11, 16, 20, 24, 32, 36, 46, 54, 59, 72, 80, 90, 106, 114, 120, 142, 152, 168, 180, 198, 212, 228, 252, 270, 276, 318, 324, 334, ...
7, 9, 14, 17, 23, 28, 35, 40, 52, 56, 70, 76, 84, 94, 112, 116, 138, 144, 162, 172, 196, 202, 222, 234, 262, 272, 298, 320, 332, 342, ...
13, 15, 21, 26, 33, 38, 47, 53, 66, 71, 83, 92, 107, 113, 130, 140, 156, 166, 190, 200, 216, 232, 256, 264, 288, 312, 328, 336, 378, ...
19, 25, 29, 37, 44, 50, 57, 68, 77, 88, 96, 110, 119, 136, 148, 160, 178, 197, 204, 226, 250, 260, 275, 294, 323, 335, 358, 380, ...
27, 31, 41, 45, 55, 64, 74, 81, 95, 100, 117, 126, 143, 155, 167, 179, 203, 208, 238, 251, 268, 286, 316, 326, 354, 359, 406, ...
39, 43, 51, 62, 69, 75, 93, 98, 115, 124, 137, 153, 164, 176, 201, 206, 236, 239, 263, 280, 300, 317, 348, 356, 392, 407,
...
49, 61, 65, 73, 86, 97, 104, 122, 131, 146, 158, 173, 191, 205, 215, 237, 257, 278, 292, 310, 333, 352, 366, 400, 417, ...
...
The initial antidiagonals are:
[1],
[2, 3],
[4, 5, 7],
[6, 8, 9, 13],
[10, 11, 14, 15, 19],
[12, 16, 17, 21, 25, 27],
[18, 20, 23, 26, 29, 31, 39],
[22, 24, 28, 33, 37, 41, 43, 49],
[30, 32, 35, 38, 44, 45, 51, 61, 63],
[34, 36, 40, 47, 50, 55, 62, 65, 67, 79],
[42, 46, 52, 53, 57, 64, 69, 73, 85, 87, 91],
[48, 54, 56, 66, 68, 74, 75, 86, 89, 99, 103, 109],
[58, 59, 70, 71, 77, 81, 93, 97, 101, 105, 121, 123, 133],
[60, 72, 76, 83, 88, 95, 98, 104, 111, 125, 127, 135, 139, 147],
...
		

References

• D. E. Knuth, Bipartite Matching, The Art of Computer Programming, Vol. 4, Pre-fascicle 14A, June 8, 2021, http://cs.stanford.edu/~knuth/fasc14a.ps.gz. See Sect. 7.5.1, Exercise 13.

Links

• D. E. Knuth, The first 32 rows

Crossrefs

Rows: A002491, A344010, A344011, ...

Columns: A000960, A100287, A344012, ...