cp's OEIS Frontend

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.

A381537 Lexicographically least sequence of natural numbers such that for all arithmetic progressions p, length(p) <= sqrt(max(p)).

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%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