A299441 Lexicographically earliest sequence of distinct positive terms such that, for any n > 1, if prime(k) is the least prime factor of a(n) then k divides a(n+1) (where prime(k) denotes the k-th prime).

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 15, 12, 13, 18, 14, 16, 17, 21, 20, 19, 24, 22, 23, 27, 26, 25, 30, 28, 29, 40, 31, 33, 32, 34, 35, 36, 37, 48, 38, 39, 42, 41, 52, 43, 56, 44, 45, 46, 47, 60, 49, 64, 50, 51, 54, 53, 80, 55, 57, 58, 59, 68, 61, 72, 62, 63

Offset

1,2

Comments

In other words, for any n > 1, A055396(a(n)) divides a(n+1).

This sequence has similarities with A285039 (especially visually).

See also A299442 for the variant involving greatest prime factors.

This sequence is a permutation of the natural numbers, with inverse A299703:

- for any n > 1, if a(n) is odd, then lpf(a(n+1)) < lpf(a(n)), and a(n+k) will be even for some k > 0 (where lpf = A020639),

- hence we have infinitely many even terms,

- and as after an even term, we can choose the least positive number not yet in the sequence, eventually every positive number will appear.

Links

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

Rémy Sigrist, PARI program for A299441

Rémy Sigrist, Scatterplot of (n, a(n)-1) for n=1..1000000

Index entries for sequences that are permutations of the natural numbers

Example

The first terms, alongside A055396(a(n)), are:
  n     a(n)    A055396(a(n))
  --    ----    -------------
   1       1       0
   2       2       1
   3       3       2
   4       4       1
   5       5       3
   6       6       1
   7       7       4
   8       8       1
   9       9       2
  10      10       1
  11      11       5
  12      15       2
  13      12       1
  14      13       6
  15      18       1
  16      14       1
  17      16       1
  18      17       7
  19      21       2
  20      20       1

Prog

(PARI) See Links section.

Crossrefs

Cf. A020639, A055396, A285039, A299442, A299703 (inverse).

Sequence in context: A211408 A107322 A194975 * A069751 A198323 A254649

Adjacent sequences: A299438 A299439 A299440 * A299442 A299443 A299444

Keyword

nonn

Author

Rémy Sigrist, Feb 10 2018

Status

approved