A364884 Triangle T(n, k), n > 0, k = 1..n, read by rows; T(1, 1) = 1, and for n > 1, k = 1..n, T(n, k) is the least unseen multiple of the k-th term of the flattened sequence .

1, 2, 4, 3, 6, 8, 5, 10, 12, 9, 7, 14, 16, 15, 18, 11, 20, 24, 21, 30, 32, 13, 22, 28, 27, 36, 40, 25, 17, 26, 44, 33, 42, 48, 35, 50, 19, 34, 52, 39, 54, 56, 45, 60, 72, 23, 38, 64, 51, 66, 80, 55, 70, 84, 63, 29, 46, 68, 57, 78, 88, 65, 90, 96, 81, 49

Offset: 1

Author

Rémy Sigrist, Aug 12 2023

Keywords

• nonn
• tabl

Comments

In other words, T(n, k) is a multiple of a(k).

As a flat sequence, this is a permutation of the positive integers (as each row starts with the least positive integer not yet in the sequence); see A364887 for the inverse permutation.

Examples

			Triangle begins:
          1,
          2,  4
          3,  6,  8
          5, 10, 12,  9
          7, 14, 16, 15,  18
         11, 20, 24, 21,  30,  32
         13, 22, 28, 27,  36,  40, 25
         17, 26, 44, 33,  42,  48, 35,  50
         19, 34, 52, 39,  54,  56, 45,  60,  72
         23, 38, 64, 51,  66,  80, 55,  70,  84, 63
         29, 46, 68, 57,  78,  88, 65,  90,  96, 81, 49
         31, 58, 76, 69, 102, 104, 75, 100, 108, 99, 77, 98
         ..................................................
    a(k)  1,  2,  4,  3,   6,   8,  5,  10,  12,  9,  7, 14
		

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 A361748 and A364885 for similar sequences.

Cf. A364887 (inverse).

Programs

PARI

See Links section.