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 A382559 #19 Apr 10 2025 05:23:31
%S A382559 1,1,2,2,2,3,3,3,3,4,4,4,3,2,4,3,3,3,3,4,4,3,4,3,3,5,5,4,3,3,3,5,3,4,
%T A382559 3,4,4,3,4,3,4,3,4,4,5,3,4,3,4,4,5,3,3,3,5,4,3,5,3,4,4,4,5,3,4,4,4,3,
%U A382559 6,4,4,4,5,3,4,6,4,4,4,4,5,4,5,3,4,6,5,4,7
%N A382559 a(n) is the length of the longest subsequence at indices in arithmetic progression ending at a(n-1) whose terms form an arithmetic progression in some order; a(1)=1.
%C A382559 First differs from A362881 at a(15).
%C A382559 This is a variant of A362881 in which the terms of an arithmetic progression can occur in any order.
%H A382559 Neal Gersh Tolunsky, <a href="/A382559/b382559.txt">Table of n, a(n) for n = 1..10000</a>
%H A382559 Neal Gersh Tolunsky, <a href="/A382559/a382559.png">Graph of the ordinal transform of the first 10000 terms</a>, with lines labeled by corresponding values of this sequence.
%e A382559 a(21) = 4: The subsequence at indices i = 2,8,14,20 (common difference 6) is {1,3,2,4} which can be rearranged to form the arithmetic progression {1,2,3,4}. We find that the longest such subsequence ending at a(20) has length 4, so a(21) = 4.
%Y A382559 Cf. A362881, A381629, A361933.
%K A382559 nonn
%O A382559 1,3
%A A382559 _Neal Gersh Tolunsky_, Apr 01 2025