This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A380495 #8 Jan 27 2025 07:31:28 %S A380495 1,2,1,3,1,2,4,3,2,5,6,2,3,4,2,7,3,2,5,4,2,3,8,2,6,3,2,4,5,2,3,9,2,4, %T A380495 3,7,5,6,3,4,10,8,3,5,4,11,3,6,7,4,3,5,9,12,3,4,6,5,3,8,4,7,3,13,5,4, %U A380495 3,6,10,9,3,4,5,7,3,6,4,8,3,5,14,4,3,11,6 %N A380495 Lexicographically earliest infinite sequence of positive integers such that consecutive occurrences of k are separated by k distinct values and each subsequence enclosed by consecutive equal values is distinct. %C A380495 Since the number of distinct terms in a subsequence is given by its enclosing values, the sequence remains the same whether we include those endpoints or not when checking the uniqueness of subsequences. %C A380495 Without the condition that subsequences enclosed by consecutive equal values are distinct, this sequence would be A001511 (the ruler function). %C A380495 Does each value occur finitely many times? %H A380495 Neal Gersh Tolunsky, <a href="/A380495/b380495.txt">Table of n, a(n) for n = 1..10000</a> %e A380495 a(7)=4: a(7) cannot be 1 because this would make a(5..7) a repeat of a(1..3) = 1,2,1. a(7) cannot be 2 or 3 as these would not enclose 2 or 3 distinct terms respectively. So a(7) must be 4. %Y A380495 Cf. A380278. %K A380495 nonn %O A380495 1,2 %A A380495 _Neal Gersh Tolunsky_, Jan 24 2025