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A344009 The Tchoukaillon array of order infinity read by downward antidiagonals. 5
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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

Table of n, a(n) for n=1..78.

D. E. Knuth, The first 32 rows

EXAMPLE

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],

...

CROSSREFS

Rows: A002491, A344010, A344011, ...

Columns: A000960, A100287, A344012, ...

Sequence in context: A267112 A269392 A166277 * A145342 A248918 A318936

Adjacent sequences:  A344006 A344007 A344008 * A344010 A344011 A344012

KEYWORD

nonn,tabl

AUTHOR

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

STATUS

approved

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Last modified October 26 05:34 EDT 2021. Contains 348256 sequences. (Running on oeis4.)