A338292 - OEIS

%I #10 Oct 26 2020 02:02:49

%S 1,2,2,3,2,3,3,3,4,2,3,4,3,3,4,4,3,4,4,4,4,5,2,3,4,4,5,3,3,4,5,4,3,4,

%T 5,5,3,4,4,5,4,4,4,5,5,4,4,5,5,5,4,5,4,5,5,5,5,5,6,2,3,4,5,5,5,6,3,3,

%U 4,5,5,6,4,3,4,5,6,4,4,4,5,6,5,3,4,5,5

%N Lexicographically earliest sequence of positive integers such that for any distinct m and n, (a(m+1-a(m)), ..., a(m)) <> (a(n+1-a(n)), ..., a(n)).

%C In other words, for any n > 0, the tuple comprising the a(n) terms up to and including a(n) is always unique.

%C This sequence is unbounded.

%C The number 1 appears once.

%C The number 2 appears after the first occurrence of a number.

%H Rémy Sigrist, <a href="/A338292/b338292.txt">Table of n, a(n) for n = 1..10000</a>

%H Rémy Sigrist, <a href="/A338292/a338292.gp.txt">PARI program for A338292</a>

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

%e   n   a(n)  (a(n+1-a(n)), ..., a(n))

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

%e    1     1  (1)

%e    2     2  (1, 2)

%e    3     2     (2, 2)

%e    4     3     (2, 2, 3)

%e    5     2           (3, 2)

%e    6     3           (3, 2, 3)

%e    7     3              (2, 3, 3)

%e    8     3                 (3, 3, 3)

%e    9     4                 (3, 3, 3, 4)

%e   10     2                          (4, 2)

%e   11     3                          (4, 2, 3)

%e   12     4                          (4, 2, 3, 4)

%e   13     3                                (3, 4, 3)

%e   14     3                                   (4, 3, 3)

%e   15     4                                   (4, 3, 3, 4)

%e   16     4                                      (3, 3, 4, 4)

%o (PARI) See Links section.

%Y See A338283 for a similar sequence.

%K nonn

%O 1,2

%A _Rémy Sigrist_, Oct 20 2020