%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+1a(m)), ..., a(m)) <> (a(n+1a(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+1a(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
