login
A372130
Lexicographically earliest sequence of distinct positive integers such that for any n > 0, a(n), a(2*n) and a(2*n+1) have distinct prime factors.
5
1, 2, 3, 5, 7, 4, 11, 6, 13, 8, 9, 15, 17, 10, 19, 23, 25, 12, 29, 21, 31, 14, 37, 16, 41, 18, 35, 27, 43, 20, 33, 22, 39, 24, 47, 49, 53, 26, 45, 32, 55, 28, 51, 57, 59, 30, 61, 63, 65, 34, 67, 71, 73, 36, 79, 38, 77, 40, 69, 81, 83, 46, 85, 75, 89, 44, 95
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.
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
See A372030 for similar sequences.
Cf. A372129 (analog based on binary 1's), A372132 (inverse).
Sequence in context: A373999 A114319 A125151 * A302024 A273665 A212646
KEYWORD
nonn
AUTHOR
Rémy Sigrist, Apr 20 2024
STATUS
approved