cp's OEIS Frontend

A380508 Lexicographically earliest sequence of positive integers such that for any n, consecutive occurrences of n are separated by a(n) distinct terms and each subsequence enclosed by consecutive equal values is distinct.

%I A380508 #11 Jan 31 2025 04:29:18
%S A380508 1,2,1,3,1,2,4,5,2,5,6,2,4,6,2,7,4,2,8,9,2,4,7,2,10,4,2,8,7,2,4,11,2,
%T A380508 10,4,7,8,12,4,11,7,10,4,8,13,7,4,14,10,8,4,7,11,15,4,10,7,8,4,14,11,
%U A380508 7,4,10,8,16,4,7,14,10,4,8,7,11,4,17,10,7,4,8,14
%N A380508 Lexicographically earliest sequence of positive integers such that for any n, consecutive occurrences of n are separated by a(n) distinct terms and each subsequence enclosed by consecutive equal values is distinct.
%C A380508 Endpoints are excluded when counting the number of distinct terms enclosed.
%C A380508 Endpoints are included when comparing subsequences enclosed.
%H A380508 Neal Gersh Tolunsky, <a href="/A380508/b380508.txt">Table of n, a(n) for n = 1..10000</a>
%e A380508 a(2) = 2, so 2's enclose 2 distinct terms. For example: a(2..6) = 2,1,3,1,2 enclosing the two distinct values in 1,3,1.
%e A380508 a(3) = 1, so 3's enclose 1 distinct term. In this case, there are no subsequences enclosed by a pair of 3s.
%e A380508 a(7) = 4: a(7) cannot be 1 as this would repeat the subsequence [1,2,1], which was seen before at a(1..3). 2 and 3 would not enclose a(2) = 2 and a(3) = 1 distinct terms respectively. So a(7) = 4, which has not occurred thus far.
%Y A380508 Cf. A363654, A380278, A380495.
%K A380508 nonn
%O A380508 1,2
%A A380508 _Neal Gersh Tolunsky_, Jan 26 2025