A331016 Lexicographically earliest sequence of distinct positive terms that can be viewed as an irregular table where the n-th row has max(1, A001221(a(n))) terms and for n > 1, T(n, k) is a multiple of the k-th prime factor of a(n) (=A027748(a(n), k)).

1, 2, 3, 4, 5, 6, 9, 12, 8, 15, 10, 18, 20, 14, 25, 16, 21, 22, 30, 24, 7, 35, 26, 27, 28, 32, 11, 34, 33, 40, 36, 39, 42, 45, 49, 38, 13, 48, 44, 56, 46, 55, 50, 17, 51, 66, 52, 60, 54, 57, 63, 65, 58, 69, 70, 72, 75, 77, 62, 19, 78, 64, 81, 68, 88, 74, 84

Offset

1,2

Comments

This sequence is a permutation of the natural numbers:

- beyond the sixth row, every even number gives rise to another even number,

- so eventually every even number appears in the sequence,

- for any odd prime number p we will have infinitely many multiples of 2*p,

- giving rise to infinitely many multiples of p,

- and eventually every number will appear.

Links

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Rémy Sigrist, PARI program for A331016

Index entries for sequences that are permutations of the natural numbers

Example

The first terms and rows are:
  n   a(n)  row(n)
  --  ----  ------------
   1     1  [1]
   2     2  [2]
   3     3  [3]
   4     4  [4]
   5     5  [5]
   6     6  [6, 9]
   7     9  [12]
   8    12  [8, 15]
   9     8  [10]
  10    15  [18, 20]
  11    10  [14, 25]

Prog

(PARI) See Links section.

Crossrefs

See A331010 for similar sequences.

Cf. A001221, A027748.

Sequence in context: A341057 A299297 A325323 * A125155 A365416 A352805

Adjacent sequences: A331013 A331014 A331015 * A331017 A331018 A331019

Keyword

nonn,look,tabf

Author

Rémy Sigrist, Jan 06 2020

Status

approved