A331018 Lexicographically earliest sequence of distinct positive terms that can be viewed as an irregular table where the n-th row has a(n) terms and for n > 1, T(n, k) is a multiple of k.

1, 2, 4, 3, 6, 9, 8, 5, 10, 12, 7, 14, 15, 16, 20, 18, 11, 22, 21, 24, 25, 30, 28, 32, 27, 13, 26, 33, 36, 35, 42, 49, 40, 17, 34, 39, 44, 45, 19, 38, 48, 52, 50, 54, 56, 64, 63, 60, 23, 46, 51, 68, 55, 66, 70, 72, 81, 80, 77, 84, 29, 58, 57, 76, 65, 78, 91

Offset: 1

Author

Rémy Sigrist, Jan 07 2020

Keywords

• nonn
• look
• tabf

Comments

This sequence is a permutation of the natural numbers as each row starts with the least value not yet in the sequence.

Examples

			The first terms and rows are:
  n   a(n)  row(n)
  --  ----  -------------------------------------
   1     1  [1]
   2     2  [2, 4]
   3     4  [3, 6, 9, 8]
   4     3  [5, 10, 12]
   5     6  [7, 14, 15, 16, 20, 18]
   6     9  [11, 22, 21, 24, 25, 30, 28, 32, 27]
   7     8  [13, 26, 33, 36, 35, 42, 49, 40]
   8     5  [17, 34, 39, 44, 45]
   9    10  [19, 38, 48, 52, 50, 54, 56, 64, 63, 60]
  10    12  [23, 46, 51, 68, 55, 66, 70, 72, 81, 80, 77, 84]
  11     7  [29, 58, 57, 76, 65, 78, 91]
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000
• Index entries for sequences that are permutations of the natural numbers
• Rémy Sigrist, PARI program for A331018

Crossrefs

See A331010 for similar sequences.

Programs

PARI

See Links section.