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Lexicographically earliest sequence of positive terms such that a(n) is the length of the n-th run of consecutive, equal terms and such that no two runs are identical.
2

%I #16 Feb 26 2020 16:07:06

%S 1,2,2,1,1,2,3,4,4,1,1,1,2,2,2,2,1,1,1,1,4,5,6,3,3,5,5,6,6,7,7,8,7,9,

%T 10,3,3,3,3,1,1,1,1,1,2,2,2,2,2,2,3,3,3,2,2,2,3,3,3,3,3,2,2,2,2,2,1,1,

%U 1,1,1,1,3,3,3,3,3,3,1,1,1,1,1,1,1,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1

%N Lexicographically earliest sequence of positive terms such that a(n) is the length of the n-th run of consecutive, equal terms and such that no two runs are identical.

%H Rémy Sigrist, <a href="/A331910/b331910.txt">Table of n, a(n) for n = 1..10000</a>

%H Rémy Sigrist, <a href="/A331910/a331910.gp.txt">PARI program for A331910</a>

%e a(8) and a(9) are 4 because runs of length 2 containing values 1 and 2 appear earlier in the sequence and because a(7) is 3.

%o (PARI) See Links section.

%Y Cf. A000002.

%K nonn

%O 1,2

%A _Samuel B. Reid_, Jan 31 2020