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

1,3

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.

Links

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Rémy Sigrist, PARI program for A345872

Example

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.

Prog

(PARI) See Links section.

Crossrefs

Cf. A345415, A345873.

Sequence in context: A142349 A234316 A284630 * A081622 A064143 A283593

Adjacent sequences: A345869 A345870 A345871 * A345873 A345874 A345875

Keyword

nonn

Author

Rémy Sigrist, Jun 27 2021

Status

approved