A372127 Lexicographically earliest sequence of distinct positive integers such that for any n > 0, a(2*n+2) = LCM(a(2*n+1), a(n+1)).

1, 2, 3, 6, 4, 12, 5, 30, 7, 28, 8, 24, 9, 45, 11, 330, 10, 70, 13, 364, 14, 56, 15, 120, 16, 144, 17, 765, 18, 198, 19, 6270, 21, 210, 20, 140, 22, 286, 23, 8372, 25, 350, 26, 728, 27, 135, 29, 3480, 31, 496, 32, 288, 33, 561, 34, 1530, 35, 630, 36, 396, 37

Offset

1,2

Comments

Conjecture: this sequence is a permutation of the positive integers.

Links

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

Rémy Sigrist, PARI program

Example

The first terms, arranged alongside a binary tree where each right child equals the least common multiple of its parent and its sibling, are:
                  |
                  1
                  |
          .-------2-------.
          |               |
      .---3---.       .---6---.
      |       |       |       |
    .-4-.   .12-.   .-5-.   .30-.
    |   |   |   |   |   |   |   |
    7  28   8  24   9  45  11 330

Prog

(PARI) \\ See Links section.

Crossrefs

See A372030 for similar sequences.

Sequence in context: A305325 A302848 A046202 * A372031 A225642 A273317

Adjacent sequences: A372124 A372125 A372126 * A372128 A372129 A372130

Keyword

nonn

Author

Rémy Sigrist, Apr 20 2024

Status

approved