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 A381537 #11 May 12 2025 19:58:10
%S A381537 1,4,5,8,9,10,12,15,16,17,18,22,23,24,25,26,28,29,30,31,33,35,36,37,
%T A381537 38,39,40,42,44,45,46,47,49,50,51,52,53,54,55,57,61,62,63,64,65,66,67,
%U A381537 68,70,71,72,73,74,75,76,81,82,83,84,85,86,87,88,90,91,92
%N A381537 Lexicographically least sequence of natural numbers such that for all arithmetic progressions p, length(p) <= sqrt(max(p)).
%C A381537 Up to a(n) the longest possible arithmetic progression is sqrt(a(n)).
%C A381537 Does the density of this sequence approach 1?
%H A381537 Samuel Harkness, <a href="/A381537/a381537.m.txt">MATLAB program</a>
%e A381537 1 is in the sequence, as 1 creates the arithmetic progression p = {1}, where length(p) = 1 and sqrt(max(p)) = 1.
%e A381537 For 2: the arithmetic progression p = {1,2} would be created. Here, length(p) = 2, and sqrt(max(p)) = sqrt(2), so length(p) > sqrt(max(p)), thus 2 is not in the sequence. Similarly, 3 is not in the sequence.
%e A381537 For 4: p = {1,4} is the only new arithmetic progression. Here, length(p) = 2, and sqrt(max(p)) = 2, so 4 is in the sequence. Similarly, 5 is in the sequence.
%e A381537 For 6: the arithmetic progression p = {4,5,6} would be created. Here, length(p) = 3, and sqrt(max(p)) = sqrt(6), so length(p) > sqrt(max(p)), thus 6 is not in the sequence.
%o A381537 (MATLAB) % See Links section.
%Y A381537 Cf. A281579, A362815.
%K A381537 nonn
%O A381537 1,2
%A A381537 _Samuel Harkness_, Feb 26 2025