A368147 - OEIS

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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

(list; graph; refs; listen; history; text; internal format)

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: