A345872 Lexicographically earliest sequence of positive integers such that the values A345415(a(n), a(n+1)) are all distinct.

1, 1, 2, 3, 5, 7, 5, 8, 11, 13, 11, 18, 23, 13, 15, 13, 21, 19, 21, 23, 18, 31, 19, 30, 37, 30, 41, 39, 23, 25, 34, 43, 28, 43, 41, 43, 45, 37, 35, 37, 50, 47, 38, 41, 54, 61, 52, 61, 59, 57, 55, 53, 64, 53, 70, 53, 76, 37, 69, 49, 66, 73, 71, 69, 71, 73, 75

Offset: 1

Author

Rémy Sigrist, Jun 27 2021

Keywords

• nonn

Comments

When writing gcd(a(n), a(n+1)) as u*a(n) + v*a(n+1) where u, v are minimal, the u's are all distinct.

Examples

			The table A345415(n, k) begins:
  n\k|  1  2   3   4
  ---+--------------
    1|  0  1   1   1
    2|  0  0  -1   1
    2|  0  1   0  -1
    2|  0  0   1   0
For n = 1:
- we can choose a(1) = 1.
For n = 2:
- we can choose a(2) = 1,
- A345415(a(1), a(2)) = 0.
For n = 3:
- a(3) must be different from 1,
- we can choose a(3) = 2,
- A345415(a(2), a(3)) = 1.
For n = 4:
- a(4) must be different from 1 and from 2,
- we can choose a(4) = 3.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000
• Rémy Sigrist, PARI program for A345872

Crossrefs

Cf. A345415, A345873.

Programs

PARI

See Links section.