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 A061369 #15 Mar 16 2025 13:10:32
%S A061369 4,9,4,9,16,25,36,9,64,81,100,25,144,169,16,49,256,289,324,81,64,441,
%T A061369 484,25,576,625,676,169,784,121,900,225,100,1089,36,289,1296,1369,196,
%U A061369 81,1600,169,1764,441,361,2025,2116,49,2304,2401,256,625,2704,2809,441
%N A061369 a(n) = smallest square in the arithmetic progression {n*k+1 : k > 0}.
%C A061369 Each square q appears in several progressions, i.e., in A000005(q-1) cases. Not necessarily as a first square. E.g., q = 81 is minimal in {10*k+1}, {20*k+1}, {40*k+1}, {80*k+1}, while not minimal in {3*k+1} and 5 other progressions. In {16*k+1} 49 comes before 81.
%H A061369 Amiram Eldar, <a href="/A061369/b061369.txt">Table of n, a(n) for n = 1..10000</a>
%F A061369 a(n) = Min{x^2 : x^2 = n*k+1}.
%F A061369 a(n) = A215653(n)^2. - _Amiram Eldar_, Mar 16 2025
%t A061369 a[n_] := Module[{m = n + 1}, While[!IntegerQ[Sqrt[m]], m += n]; m]; Array[a, 55] (* _Amiram Eldar_, Mar 16 2025 *)
%o A061369 (PARI) a(n) = {my(m = n + 1); while(!issquare(m), m += n); m;} \\ _Amiram Eldar_, Mar 16 2025
%Y A061369 Cf. A000005, A215653.
%K A061369 nonn
%O A061369 1,1
%A A061369 _Labos Elemer_, Jun 08 2001