OFFSET
1,2
COMMENTS
In other words, for any n > 0, exactly one of gcd(a(n), a(n+1)), gcd(a(n), a(n+2)), gcd(a(n+1), a(n+2)) is strictly greater than 1.
This sequence has connections with the Yellowstone permutation (A098550).
Conjecture: this sequence is a permutation of the natural numbers.
LINKS
Rémy Sigrist, Table of n, a(n) for n = 1..10000
Rémy Sigrist, PARI program for A338619
EXAMPLE
The first terms, alongside associated GCD's, are:
n a(n) gcd(a(n),a(n+1)) gcd(a(n),a(n+2)) gcd(a(n+1),a(n+2))
-- ---- ---------------- ---------------- ------------------
1 1 1 1 2
2 2 2 1 1
3 4 1 4 1
4 3 1 3 1
5 8 1 2 1
6 9 1 1 5
7 10 5 1 1
8 5 1 1 7
9 7 7 1 1
10 14 1 2 1
PROG
(PARI) See Links section.
CROSSREFS
KEYWORD
nonn
AUTHOR
Rémy Sigrist, Nov 04 2020
STATUS
approved