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A366303
Square array A(n, k), n, k > 0, read and filled by upwards antidiagonals the greedy way with distinct positive integers such that any two distinct terms in the same row or column are coprime.
2
1, 2, 3, 5, 7, 4, 9, 8, 11, 13, 17, 19, 21, 15, 23, 29, 25, 31, 37, 41, 35, 43, 47, 53, 14, 59, 61, 67, 49, 71, 65, 73, 55, 79, 83, 89, 97, 101, 103, 107, 6, 109, 113, 127, 121, 131, 137, 139, 149, 119, 143, 151, 157, 163, 167, 169, 173, 179, 181, 191, 12, 133, 193, 197, 199, 211
OFFSET
1,2
COMMENTS
This sequence is a variant of A366030, with one less constraint.
All the prime numbers appear in the sequence, in ascending order.
For any prime number p, the first multiple of p in the sequence is p.
Will every positive integer appear in the sequence?
LINKS
Rémy Sigrist, Colored representation of the array for n, k <= 881 (grayish pixels correspond to prime numbers)
Rémy Sigrist, PARI program
EXAMPLE
Array A(n, k) begins:
n\k | 1 2 3 4 5 6 7 8 9 10
----+-------------------------------------------------
1 | 1 3 4 13 23 35 67 89 121 167
2 | 2 7 11 15 41 61 83 127 163 199
3 | 5 8 21 37 59 79 113 157 197 247
4 | 9 19 31 14 55 109 151 193 221 307
5 | 17 25 53 73 6 143 133 241 293 353
6 | 29 47 65 107 119 12 239 283 349 401
7 | 43 71 103 149 191 233 10 33 161 463
8 | 49 101 139 181 229 281 27 16 95 451
9 | 97 137 179 227 277 323 341 91 18 115
10 | 131 173 223 253 347 397 461 85 613 24
PROG
(PARI) See Links section.
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Rémy Sigrist, Oct 06 2023
STATUS
approved