A366030 - OEIS

A366030

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 or antidiagonal are coprime.

%I #13 Oct 08 2023 08:58:45

%S 1,2,3,5,7,4,9,8,11,13,17,19,21,23,25,29,31,37,41,27,43,47,53,59,10,

%T 61,67,49,71,55,73,57,79,83,89,97,77,101,103,107,16,109,113,65,127,

%U 131,137,85,139,91,121,149,151,157,163,167,169,173,179,181,6,115,119,191,193,197

%N 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 or antidiagonal are coprime.

%C This sequence is a variant of A284145 (with one less constraint).

%C All the prime numbers appear in the sequence, in ascending order.

%C For any prime number p, the first multiple of p in the sequence is p.

%C Will every positive integer appear in the sequence?

%H Rémy Sigrist, <a href="/A366030/a366030.png">Colored representation of the array for n, k <= 500</a> (grayish pixels correspond to prime numbers)

%H Rémy Sigrist, <a href="/A366030/a366030.gp.txt">PARI program</a>

%e Array A(n, k) begins:

%e n\k| 1 2 3 4 5 6 7 8 9 10

%e ---+-------------------------------------------------

%e 1| 1 3 4 13 25 43 49 97 127 163

%e 2| 2 7 11 23 27 67 89 65 157 193

%e 3| 5 8 21 41 61 83 113 151 191 221

%e 4| 9 19 37 10 79 109 149 119 239 281

%e 5| 17 31 59 57 16 121 115 233 203 347

%e 6| 29 53 73 107 91 6 229 277 337 125

%e 7| 47 55 103 139 181 161 12 331 323 463

%e 8| 71 101 85 179 209 271 317 18 403 259

%e 9| 77 137 173 227 269 95 377 461 24 613

%e 10| 131 169 223 187 313 397 457 437 185 32

%o (PARI) See Links section.

%Y Cf. A284145, A366031, A366303.

%K nonn,tabl

%O 1,2

%A _Rémy Sigrist_, Sep 26 2023