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A338618
Lexicographically earliest sequence of distinct positive integers such that three consecutive terms are never pairwise coprime.
2
1, 2, 4, 3, 6, 5, 8, 10, 7, 12, 9, 11, 15, 18, 13, 14, 16, 17, 20, 22, 19, 24, 21, 23, 27, 30, 25, 26, 28, 29, 32, 34, 31, 36, 33, 35, 39, 40, 38, 37, 42, 44, 41, 46, 48, 43, 45, 50, 47, 52, 54, 49, 51, 56, 57, 58, 60, 53, 55, 65, 59, 70, 62, 61, 64, 66, 63
OFFSET
1,2
COMMENTS
In other words, for any n > 0, at least 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 2 3
4 3 3 1 1
5 6 1 2 1
6 5 1 5 2
7 8 2 1 1
8 10 1 2 1
9 7 1 1 3
10 12 3 1 1
PROG
(PARI) See Links section.
CROSSREFS
See A338619 for a similar sequence.
Sequence in context: A343012 A143692 A337116 * A114792 A113324 A338362
KEYWORD
nonn
AUTHOR
Rémy Sigrist, Nov 04 2020
STATUS
approved