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A338619
Lexicographically earliest sequence of distinct positive terms such that among three consecutive terms there is exactly one pair of terms that are not coprime.
2
1, 2, 4, 3, 8, 9, 10, 5, 7, 14, 11, 6, 12, 13, 15, 18, 17, 16, 20, 19, 22, 24, 23, 21, 27, 25, 33, 35, 28, 29, 26, 30, 31, 32, 34, 37, 36, 38, 41, 40, 42, 43, 39, 45, 44, 46, 47, 48, 50, 49, 52, 54, 53, 51, 57, 55, 63, 56, 59, 58, 60, 61, 62, 64, 65, 66, 68
OFFSET
1,2
COMMENTS
In other words, for any n > 0, exactly one of gcd(a(n), a(n+1)), gcd(a(n), a(n+2)), gcd(a(n+1), a(n+2)) is strictly greater than 1.
This sequence has connections with the Yellowstone permutation (A098550).
Conjecture: this sequence is a permutation of the natural numbers.
LINKS
EXAMPLE
The first terms, alongside associated GCD's, are:
n a(n) gcd(a(n),a(n+1)) gcd(a(n),a(n+2)) gcd(a(n+1),a(n+2))
-- ---- ---------------- ---------------- ------------------
1 1 1 1 2
2 2 2 1 1
3 4 1 4 1
4 3 1 3 1
5 8 1 2 1
6 9 1 1 5
7 10 5 1 1
8 5 1 1 7
9 7 7 1 1
10 14 1 2 1
PROG
(PARI) See Links section.
CROSSREFS
See A338618 for a similar sequence.
Sequence in context: A332214 A285322 A129593 * A279355 A279356 A241909
KEYWORD
nonn
AUTHOR
Rémy Sigrist, Nov 04 2020
STATUS
approved