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 A077224 #17 Aug 22 2023 08:00:36
%S A077224 1,2,4,9,13,29,33,101,105,109,157,177,253,289,301,353,409,429,465,501,
%T A077224 533,553,589,609,681,753,877,933,965,1153,1477,1905,1977,2101,2125,
%U A077224 2229,2305,2405,2605,2657,2801,2913,3305,3381,3489,3565,3777,3781,3881,4029
%N A077224 a(0) = 1; for n > 1, a(n) = smallest number > a(n-1) such that a(n) + a(k) is squarefree for k = 1 to n-1.
%C A077224 Or, sum of any two terms is a squarefree number.
%H A077224 Amiram Eldar, <a href="/A077224/b077224.txt">Table of n, a(n) for n = 0..1800</a>
%F A077224 It can easily be proved that a(n) == 1 mod 4 for all n > 3.
%e A077224 13 is a member as 13 + 1, 13 + 2, 13 + 4, 13 + 9 are all squarefree.
%t A077224 a[0] = 1; a[n_] := a[n] = Module[{t = Array[a, n, 0], k = a[n - 1] + 1}, While[AnyTrue[t, ! SquareFreeQ[k + #] &], k++]; k]; Array[a, 100, 0] (* _Amiram Eldar_, Aug 21 2023 *)
%Y A077224 Cf. A005117, A077225, A080793, A085902.
%K A077224 nonn
%O A077224 0,2
%A A077224 _Amarnath Murthy_, Nov 03 2002
%E A077224 Edited by _Sam Alexander_, Dec 12 2003