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Lexicographically earliest sequence of positive integers such that the pairs (a(n) mod a(n+1), a(n+1)) are all distinct.
5

%I #13 Aug 04 2024 12:43:20

%S 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 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 10,13,11,11,12,11,13,12,12,13,13,14,9,14,10,14,11

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

%C The value 1 appears twice; for any v > 1, v appears v times.

%C This sequence shares graphical features with A335943.

%H Rémy Sigrist, <a href="/A375110/b375110.txt">Table of n, a(n) for n = 1..10000</a>

%H Rémy Sigrist, <a href="/A375110/a375110.gp.txt">PARI program</a>

%e The first terms, alongside the corresponding pairs, are:

%e n a(n) (a(n) mod a(n+1), a(n+1))

%e -- ---- -------------------------

%e 1 1 (0, 1)

%e 2 1 (1, 2)

%e 3 2 (0, 2)

%e 4 2 (2, 3)

%e 5 3 (0, 3)

%e 6 3 (3, 4)

%e 7 4 (1, 3)

%e 8 3 (3, 5)

%e 9 5 (1, 4)

%e 10 4 (0, 4)

%e 11 4 (4, 5)

%e 12 5 (0, 5)

%e 13 5 (5, 6)

%e 14 6 (2, 4)

%e 15 4 (4, 6)

%o (PARI) \\ See Links section.

%Y See A375114 and A375115 for similar sequences.

%Y Cf. A335943, A375111, A375112.

%K nonn

%O 1,3

%A _Rémy Sigrist_, Jul 30 2024