A299440 Lexicographically earliest sequence of distinct positive terms such that, for any n > 0, if prime(k) divides a(n) then k divides a(n+1) (where prime(k) denotes the k-th prime).

1, 2, 3, 4, 5, 6, 8, 7, 12, 10, 9, 14, 16, 11, 15, 18, 20, 21, 24, 22, 25, 27, 26, 30, 36, 28, 32, 13, 42, 40, 33, 50, 39, 48, 34, 35, 60, 54, 38, 56, 44, 45, 66, 70, 72, 46, 63, 52, 78, 84, 64, 17, 49, 68, 77, 80, 51, 98, 76, 88, 55, 75, 90, 96, 58, 100, 57

Offset

1,2

Comments

In other words, for any n > 0, A290103(a(n)) divides a(n+1).

See also A299441 (where we consider only least prime factors) and A299442 (where we consider only greatest prime factors).

Links

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

Rémy Sigrist, PARI program for A299440

Example

The first terms, alongside A290103(a(n)), are:
  n     a(n)  A290103(a(n))
  --    ----  -------------
   1       1      1
   2       2      1
   3       3      2
   4       4      1
   5       5      3
   6       6      2
   7       8      1
   8       7      4
   9      12      2
  10      10      3
  11       9      2
  12      14      4
  13      16      1
  14      11      5
  15      15      6
  16      18      2
  17      20      3
  18      21      4
  19      24      2
  20      22      5

Prog

(PARI) See Links section.

Crossrefs

Cf. A290103, A299441, A299442.

Sequence in context: A339607 A262374 A299442 * A330401 A145518 A256221

Adjacent sequences: A299437 A299438 A299439 * A299441 A299442 A299443

Keyword

nonn

Author

Rémy Sigrist, Feb 10 2018

Status

approved