login
A320123
a(1) = 1, a(2) = 2, a(3) = 3, and for any n > 3, a(n) = the smallest positive integer not yet in the sequence such that gcd(a(n-2), a(n-1)), gcd(a(n-1), a(n)) and gcd(a(n), a(n-2)) are all distinct.
1
1, 2, 3, 6, 4, 9, 12, 8, 15, 10, 14, 5, 20, 16, 25, 30, 18, 27, 22, 24, 11, 33, 21, 7, 36, 28, 35, 26, 40, 13, 52, 32, 39, 42, 34, 17, 38, 68, 19, 76, 44, 55, 45, 48, 46, 23, 50, 92, 60, 51, 56, 54, 49, 63, 57, 70, 66, 65, 75, 69, 80, 72, 78, 64, 81, 84, 58
OFFSET
1,2
COMMENTS
This sequence is a variant of A127202.
The sequence is well defined as for any n > 3, provided the first n terms are known, any number v of the form a(n-2) * b where b is coprime to a(n) * a(n-1) satisfies #{ gcd(a(n-1), a(n)), gcd(a(n), v), gcd(v, a(n-1)) } = #{ gcd(a(n-1), a(n)), gcd(a(n), a(n-2)), gcd(a(n-2), a(n-1)) } = 3, and a(n+1) exists.
In the scatterplot of the sequence, the prime numbers correspond to the lower line.
LINKS
EXAMPLE
The first terms, alongside gcd(a(n-2), a(n-1)), gcd(a(n-1), a(n)) and gcd(a(n), a(n-2)), are:
n a(n) gcd(a(n-2),a(n-1)) gcd(a(n-1),a(n)) gcd(a(n),a(n-2))
-- ---- ------------------ ---------------- ----------------
1 1 N/A N/A N/A
2 2 N/A 1 N/A
3 3 1 1 1
4 6 1 3 2
5 4 3 2 1
6 9 2 1 3
7 12 1 3 4
8 8 3 4 1
9 15 4 1 3
10 10 1 5 2
11 14 5 2 1
12 5 2 1 5
13 20 1 5 2
14 16 5 4 1
15 25 4 1 5
PROG
(PARI) See Links section.
CROSSREFS
Cf. A127202.
Sequence in context: A152679 A232561 A348395 * A363444 A194357 A165783
KEYWORD
nonn
AUTHOR
Rémy Sigrist, Oct 06 2018
STATUS
approved