A338444 Lexicographically earliest sequence of distinct squarefree numbers such that for any prime p, any run of consecutive multiples of p has length exactly 2.

1, 2, 6, 3, 5, 10, 14, 7, 11, 22, 26, 13, 15, 30, 34, 17, 19, 38, 42, 21, 23, 46, 58, 29, 31, 62, 66, 33, 35, 70, 74, 37, 39, 78, 82, 41, 43, 86, 94, 47, 51, 102, 106, 53, 55, 110, 114, 57, 59, 118, 122, 61, 65, 130, 134, 67, 69, 138, 142, 71, 73, 146, 154, 77

Offset

1,2

Comments

This sequence is a squarefree variant of A280864.

Conjecture: this sequence is a permutation of the squarefree numbers (A005117).

Links

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

Rémy Sigrist, C program for A338444

Example

The first terms, alongside their prime factors, are:
  n   a(n)  Prime factors
  --  ----  -------------
   1     1
   2     2  2
   3     6  2 3
   4     3    3
   5     5      5
   6    10  2   5
   7    14  2     7
   8     7        7
   9    11          11
  10    22  2       11
  11    26  2         13
  12    13            13
  13    15    3 5
  14    30  2 3 5
  15    34  2           17
  16    17              17

Prog

(C) // See Links section.

Crossrefs

Cf. A005117, A280864, A338441.

Sequence in context: A064433 A163338 A323335 * A139384 A083481 A177209

Adjacent sequences: A338441 A338442 A338443 * A338445 A338446 A338447

Keyword

nonn

Author

Rémy Sigrist, Oct 28 2020

Status

approved