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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.

%I A375114 #10 Aug 04 2024 12:42:52
%S A375114 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,
%T A375114 12,13,12,14,14,15,10,15,14,16,16,17,16,18,12,15,15,18,18,19,18,20,16,
%U A375114 20,20,21,14,21,20,22,11,22,22,23,22,24,16,24,18,21
%N A375114 Lexicographically earliest sequence of positive integers such that the pairs (gcd(a(n), a(n+1)), a(n+1)) are all distinct.
%C A375114 The value 1 appears twice; for any v > 1, the value v appears A000005(v) times.
%H A375114 Rémy Sigrist, <a href="/A375114/b375114.txt">Table of n, a(n) for n = 1..10000</a>
%H A375114 Rémy Sigrist, <a href="/A375114/a375114.gp.txt">PARI program</a>
%e A375114 The first terms, alongside the corresponding pairs, are:
%e A375114   n   a(n)  (gcd(a(n), a(n+1)), a(n+1))
%e A375114   --  ----  ---------------------------
%e A375114    1     1  (1, 1)
%e A375114    2     1  (1, 2)
%e A375114    3     2  (2, 2)
%e A375114    4     2  (1, 3)
%e A375114    5     3  (3, 3)
%e A375114    6     3  (1, 4)
%e A375114    7     4  (4, 4)
%e A375114    8     4  (1, 5)
%e A375114    9     5  (5, 5)
%e A375114   10     5  (1, 6)
%e A375114   11     6  (2, 4)
%e A375114   12     4  (2, 6)
%e A375114   13     6  (6, 6)
%e A375114   14     6  (1, 7)
%e A375114   15     7  (7, 7)
%o A375114 (PARI) \\ See Links section.
%Y A375114 See A375110 for similar sequences.
%Y A375114 Cf. A000005.
%K A375114 nonn
%O A375114 1,3
%A A375114 _Rémy Sigrist_, Jul 30 2024