A375005 Lexicographically earliest infinite sequence of distinct positive integers such that two consecutive terms always have some common prime factor and for any prime number p, any run of consecutive multiples of p has length exactly 2.

2, 6, 15, 10, 12, 21, 14, 18, 33, 22, 20, 35, 28, 24, 39, 26, 30, 105, 56, 34, 51, 36, 38, 57, 42, 70, 45, 48, 40, 55, 44, 46, 69, 54, 50, 65, 52, 58, 87, 60, 110, 77, 63, 66, 154, 91, 78, 84, 119, 68, 62, 93, 72, 74, 111, 75, 80, 76, 95, 85, 102, 90, 115, 92

Offset: 1

Author

Rémy Sigrist, Jul 27 2024

Keywords

• nonn

Comments

This sequence combines features of A064413 and A280864.

The leading term a(1) = 2 is the only prime power in the sequence.

Will every term of A024619 appear?

Examples

			The first terms, alongside their prime factors, are:
  n   a(n)  prime factors
  --  ----  -------------
   1     2  2
   2     6  2 3
   3    15    3 5
   4    10  2   5
   5    12  2 3
   6    21    3   7
   7    14  2     7
   8    18  2 3
   9    33    3     11
  10    22  2       11
  11    20  2   5
  12    35      5 7
  13    28  2     7
  14    24  2 3
  15    39    3        13
  16    26  2          13
		

Links

• Rémy Sigrist, PARI program

Crossrefs

Cf. A024619, A064413, A280864.

Programs

PARI

\\ See Links section.