A372031 Lexicographically earliest sequence of distinct positive integers such that for any n > 0, a(2*n+2) = a(2*n+1) * a(n+1).

1, 2, 3, 6, 4, 12, 5, 30, 7, 28, 8, 96, 9, 45, 10, 300, 11, 77, 13, 364, 14, 112, 15, 1440, 16, 144, 17, 765, 18, 180, 19, 5700, 20, 220, 21, 1617, 22, 286, 23, 8372, 24, 336, 25, 2800, 26, 390, 27, 38880, 29, 464, 31, 4464, 32, 544, 33, 25245, 34, 612, 35

Offset

1,2

Comments

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

For any prime number p, the first multiple of p in the sequence is precisely p.

Links

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

Rémy Sigrist, Colored logarithmic scatterplot of the first 100000 terms (where the color is function of A007814(n), the 2-adic valuation of n)

Rémy Sigrist, PARI program

Example

The first terms, arranged alongside a binary tree where each right child equals its parent times its sibling, are:
                    |
                    1
                    |
            .-------2-------.
            |               |
        .---3---.       .---6---.
        |       |       |       |
      .-4-.   .12-.   .-5-.   .30-.
      |   |   |   |   |   |   |   |
      7  28   8  96   9  45  10 300

Prog

(PARI) \\ See Links section.

Crossrefs

See A372030 for similar sequences.

Cf. A007814.

Sequence in context: A302848 A046202 A372127 * A225642 A273317 A328443

Adjacent sequences: A372028 A372029 A372030 * A372032 A372033 A372034

Keyword

nonn

Author

Rémy Sigrist, Apr 16 2024

Status

approved