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

1,1

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?

Links

Table of n, a(n) for n=1..64.

Rémy Sigrist, PARI program

Example

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

Prog

(PARI) \\ See Links section.

Crossrefs

Cf. A024619, A064413, A280864.

Sequence in context: A133933 A297574 A349984 * A215081 A348592 A337737

Adjacent sequences: A375002 A375003 A375004 * A375006 A375007 A375008

Keyword

nonn

Author

Rémy Sigrist, Jul 27 2024

Status

approved