A334766 Lexicographically earliest sequence of distinct positive integers such that for any n > 0, the prime tower factorization of a(n+1) can be obtained from that of a(n) by adding or removing exactly one prime number.

1, 2, 4, 12, 6, 3, 9, 18, 36, 144, 48, 16, 80, 20, 10, 5, 15, 30, 60, 180, 90, 45, 225, 75, 25, 50, 100, 300, 150, 450, 900, 3600, 720, 240, 1200, 400, 2800, 560, 112, 28, 14, 7, 21, 42, 84, 252, 126, 63, 315, 105, 35, 70, 140, 420, 210, 630, 1260, 5040, 1008

Offset

1,2

Comments

The prime tower factorization of a number is defined in A182318.

For any n > 0, a(n+1) is either a multiple or a divisor of a(n).

For any prime number p, the sequence contains a multiple of p.

Links

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

Rémy Sigrist, PARI program for A334766

Formula

abs(A106490(a(n+1)) - A106490(a(n))) = 1.

Example

The first terms, alongside their prime tower factorizations, are:
  n   a(n)  Prime tower factorization of a(n)
  --  ----  ---------------------------------
   1     1  1
   2     2  2
   3     4  2^2
   4    12  2^2   * 3
   5     6  2     * 3
   6     3          3
   7     9          3^2
   8    18  2     * 3^2
   9    36  2^2   * 3^2
  10   144  2^2^2 * 3^2
  11    48  2^2^2 * 3
  12    16  2^2^2
  13    80  2^2^2       * 5
  14    20  2^2         * 5
  15    10  2           * 5
  16     5                5

Prog

(PARI) See Links section.

Crossrefs

Cf. A106490, A182318, A298480.

Sequence in context: A365000 A294103 A137369 * A336847 A338118 A294063

Adjacent sequences: A334763 A334764 A334765 * A334767 A334768 A334769

Keyword

nonn

Author

Rémy Sigrist, May 10 2020

Status

approved