A368147 Lexicographically earliest sequence of positive integers such that for any n > 0, a(n) = a(2*n), a(n) and a(n+1) are coprime, and all pairs of adjacent terms are distinct.

1, 1, 2, 1, 3, 2, 3, 1, 4, 3, 5, 2, 5, 3, 4, 1, 5, 4, 7, 3, 7, 5, 7, 2, 9, 5, 8, 3, 11, 4, 5, 1, 6, 5, 9, 4, 9, 7, 10, 3, 8, 7, 8, 5, 6, 7, 9, 2, 11, 9, 11, 5, 11, 8, 11, 3, 10, 11, 7, 4, 13, 5, 12, 1, 7, 6, 17, 5, 13, 9, 13, 4, 17, 9, 10, 7, 1, 10, 13, 3, 13

Offset

1,3

Comments

This sequence has similarities with Stern's diatomic series (A002487) as it equals its even bisection and two consecutive terms are always coprime.

Will n -> (a(n), a(n+1)) run through all pairs of coprime integers?

Links

Table of n, a(n) for n=1..81.

Rémy Sigrist, Colored scatterplot of (a(n), a(n+1)) for n < 2^18 (where the color is function of n)

Rémy Sigrist, PARI program

Example

The first terms, alongside pairs of successive terms following the introduction of odd-indexed terms, are:
  n   a(n)  New pairs
  --  ----  --------------
   1     1  (1, 1)
   2     1
   3     2  (1, 2), (2, 1)
   4     1
   5     3  (1, 3), (3, 2)
   6     2
   7     3  (2, 3), (3, 1)
   8     1
   9     4  (1, 4), (4, 3)
  10     3
  11     5  (3, 5), (5, 2)
  12     2
  13     5  (2, 5), (5, 3)
  14     3

Prog

(PARI) See Links section.

Crossrefs

Cf. A002487, A368071.

Sequence in context: A294442 A281392 A287051 * A002487 A318509 A357980

Adjacent sequences: A368144 A368145 A368146 * A368148 A368149 A368150

Keyword

nonn

Author

Rémy Sigrist, Dec 13 2023

Status

approved