A365230 Triangle T(n, k), n > 0, k = 1..n, read by rows and filled the greedy way with distinct positive integers such that T(n, k) is a multiple of T(k, 1).

1, 2, 4, 3, 6, 9, 5, 8, 12, 10, 7, 14, 15, 20, 21, 11, 16, 18, 25, 28, 22, 13, 24, 27, 30, 35, 33, 26, 17, 32, 36, 40, 42, 44, 39, 34, 19, 38, 45, 50, 49, 55, 52, 51, 57, 23, 46, 48, 60, 56, 66, 65, 68, 76, 69, 29, 54, 63, 70, 77, 88, 78, 85, 95, 92, 58

Offset: 1

Author

Rémy Sigrist, Aug 27 2023

Keywords

• nonn
• tabl

Comments

As a flat sequence, this is a permutation of the positive integers (as each row starts with the least value not yet in the sequence); see A365231 for the inverse.

Examples

			Triangle T(n, k) begins:
         1;
         2,  4;
         3,  6,  9;
         5,  8, 12, 10;
         7, 14, 15, 20, 21;
        11, 16, 18, 25, 28, 22;
        13, 24, 27, 30, 35, 33, 26;
        17, 32, 36, 40, 42, 44, 39, 34;
        19, 38, 45, 50, 49, 55, 52, 51, 57;
        ...................................
T(k, 1)  1   2   3   5   7  11  13  17  19
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10011 (rows for n = 1..141 flattened)
• Rémy Sigrist, PARI program
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

See A364884 and A365232 for similar sequences.

Cf. A365231 (inverse).

Programs

PARI

See Links section.