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A377151
Lexicographically earliest sequence of distinct positive integers such that for any n > 1, a(n) is a multiple or a divisor of a(floor(n/2)).
1
1, 2, 3, 4, 6, 9, 12, 8, 16, 18, 24, 27, 36, 48, 60, 32, 40, 64, 80, 54, 72, 96, 120, 81, 108, 144, 180, 192, 240, 5, 10, 128, 160, 20, 200, 256, 320, 400, 480, 162, 216, 288, 360, 384, 576, 15, 30, 243, 324, 432, 540, 720, 864, 45, 90, 768, 960, 1200, 1440
OFFSET
1,2
COMMENTS
This sequence can be seen as an infinite complete binary tree where each node (except the root node) is a multiple or a divisor of its parent.
Will every integer appear in the sequence?
If we have a multiple of a prime number p, then the sequence contains p, and a multiple of q for any prime number q < p.
LINKS
Rémy Sigrist, PARI program
EXAMPLE
The first terms (arranged as a binary tree) are:
|
a(1) .-------------1-------------.
| |
a(2-3) .------2------. .------3------.
| | | |
a(4-7) .---4--. .---6--. .---9--. .--12--.
| | | | | | | |
a(8-15) 8 16 18 24 27 36 48 60
PROG
(PARI) \\ See Links section.
CROSSREFS
Sequence in context: A338914 A048249 A370843 * A288734 A332034 A332035
KEYWORD
nonn,new
AUTHOR
Rémy Sigrist, Oct 18 2024
STATUS
approved