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A375114
Lexicographically earliest sequence of positive integers such that the pairs (gcd(a(n), a(n+1)), a(n+1)) are all distinct.
2
1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 4, 6, 6, 7, 7, 8, 8, 9, 6, 8, 10, 10, 11, 10, 12, 8, 12, 9, 9, 12, 12, 13, 12, 14, 14, 15, 10, 15, 14, 16, 16, 17, 16, 18, 12, 15, 15, 18, 18, 19, 18, 20, 16, 20, 20, 21, 14, 21, 20, 22, 11, 22, 22, 23, 22, 24, 16, 24, 18, 21
OFFSET
1,3
COMMENTS
The value 1 appears twice; for any v > 1, the value v appears A000005(v) times.
LINKS
Rémy Sigrist, PARI program
EXAMPLE
The first terms, alongside the corresponding pairs, are:
n a(n) (gcd(a(n), a(n+1)), a(n+1))
-- ---- ---------------------------
1 1 (1, 1)
2 1 (1, 2)
3 2 (2, 2)
4 2 (1, 3)
5 3 (3, 3)
6 3 (1, 4)
7 4 (4, 4)
8 4 (1, 5)
9 5 (5, 5)
10 5 (1, 6)
11 6 (2, 4)
12 4 (2, 6)
13 6 (6, 6)
14 6 (1, 7)
15 7 (7, 7)
PROG
(PARI) \\ See Links section.
CROSSREFS
See A375110 for similar sequences.
Cf. A000005.
Sequence in context: A104103 A194964 A029923 * A096029 A206915 A327247
KEYWORD
nonn
AUTHOR
Rémy Sigrist, Jul 30 2024
STATUS
approved