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A375110 Lexicographically earliest sequence of positive integers such that the pairs (a(n) mod a(n+1), a(n+1)) are all distinct.

%I A375110 #13 Aug 04 2024 12:43:20
%S A375110 1,1,2,2,3,3,4,3,5,4,4,5,5,6,4,6,5,7,5,8,6,6,7,6,8,7,7,8,8,9,6,9,7,9,
%T A375110 8,10,7,10,8,11,7,11,8,12,8,13,9,9,10,9,11,9,12,9,13,10,10,11,10,12,
%U A375110 10,13,11,11,12,11,13,12,12,13,13,14,9,14,10,14,11
%N A375110 Lexicographically earliest sequence of positive integers such that the pairs (a(n) mod a(n+1), a(n+1)) are all distinct.
%C A375110 The value 1 appears twice; for any v > 1, v appears v times.
%C A375110 This sequence shares graphical features with A335943.
%H A375110 Rémy Sigrist, <a href="/A375110/b375110.txt">Table of n, a(n) for n = 1..10000</a>
%H A375110 Rémy Sigrist, <a href="/A375110/a375110.gp.txt">PARI program</a>
%e A375110 The first terms, alongside the corresponding pairs, are:
%e A375110   n   a(n)  (a(n) mod a(n+1), a(n+1))
%e A375110   --  ----  -------------------------
%e A375110    1     1  (0, 1)
%e A375110    2     1  (1, 2)
%e A375110    3     2  (0, 2)
%e A375110    4     2  (2, 3)
%e A375110    5     3  (0, 3)
%e A375110    6     3  (3, 4)
%e A375110    7     4  (1, 3)
%e A375110    8     3  (3, 5)
%e A375110    9     5  (1, 4)
%e A375110   10     4  (0, 4)
%e A375110   11     4  (4, 5)
%e A375110   12     5  (0, 5)
%e A375110   13     5  (5, 6)
%e A375110   14     6  (2, 4)
%e A375110   15     4  (4, 6)
%o A375110 (PARI) \\ See Links section.
%Y A375110 See A375114 and A375115 for similar sequences.
%Y A375110 Cf. A335943, A375111, A375112.
%K A375110 nonn
%O A375110 1,3
%A A375110 _Rémy Sigrist_, Jul 30 2024