OFFSET
1,2
COMMENTS
This sequence is a permutation of the positive integers with inverse A372132:
- for any prime number p, the first multiple of p is precisely p,
- all prime numbers appear in the sequence, in increasing order,
- for any v > 0, each prime number not dividing v provides an opportunity to select v later, and eventually v will appear in the sequence.
LINKS
Rémy Sigrist, Table of n, a(n) for n = 1..10001
Rémy Sigrist, PARI program
FORMULA
GCD(a(n), a(2*n)) = GCD(a(n), a(2*n+1)) = GCD(a(2*n), a(2*n+1)) = 1 for any n > 0.
EXAMPLE
The first terms, arranged alongside a binary tree where siblings have distinct prime factors and parent and children have distinct prime factors, are:
|
.-------1-------.
| |
.---2---. .---3---.
| | | |
.-5-. .-7-. .-4-. .11-.
| | | | | | | |
6 13 8 9 15 17 10 19
PROG
(PARI) \\ See Links section.
CROSSREFS
KEYWORD
nonn
AUTHOR
Rémy Sigrist, Apr 20 2024
STATUS
approved