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 A256173 #38 Sep 06 2023 16:16:51
%S A256173 0,1,3,4,5,8,9,12,15,16,21,24,25,27,32,35,36,40,45,48,49,55,60,63,64,
%T A256173 65,72,77,80,81,84,91,96,99,100,105,112,117,120,121,128,135,140,143,
%U A256173 144,153,160,165,168,169,171,180,187,192,195,196,200,209,216,221,224,225,231,240,247,252,255,256,264,273,280,285,288,289,299
%N A256173 Numbers k such that ceiling(sqrt(k))^2 - k is a square.
%C A256173 Numbers k such that A068527(k) is a square. k is in the sequence if and only if k - ceiling(sqrt(k))^2 + ceiling(sqrt(ceiling(sqrt(k))^2 - k))^2 = 0.
%C A256173 A000290 is a subsequence since for a square k, ceiling(sqrt(k))^2 - k = 0, a square too.
%C A256173 Also, numbers k such that A249298(k) is 1.
%C A256173 Also, numbers k such that A249142(k) is 0.
%C A256173 The only prime numbers in the sequence are 3 and 5.
%C A256173 No number from A016825 appears in the sequence.
%C A256173 If p and q are terms of A065091 and if q satisfies the inequality p - 2*sqrt(2p) + 2 < q < p + 2*sqrt(2p) + 2, then p*q is in the sequence. Thus infinitely many numbers from A046315 appear in the sequence.
%e A256173 Ceiling(sqrt(27))^2 - 27 = 9 = 3^2, so 27 is in the sequence.
%t A256173 Flatten[Position[Table[n - Ceiling[Sqrt[n]]^2 + Ceiling[Sqrt[-n + Ceiling[Sqrt[n]]^2]]^2, {n, 0, 300}], 0]] - 1
%t A256173 Select[Range[0,300],IntegerQ[Sqrt[Ceiling[Sqrt[#]]^2-#]]&] (* _Harvey P. Dale_, Sep 06 2023 *)
%o A256173 (PARI) isok(n) = issquare(ceil(sqrt(n))^2-n); \\ _Michel Marcus_, Mar 18 2015
%o A256173 (Magma) [n: n in [0..200] | IsSquare(Ceiling(Sqrt(n))^2-n)]; // _Vincenzo Librandi_, Mar 18 2015
%Y A256173 Cf. A000290, A068527, A145236, A249142, A249298, A046315.
%K A256173 nonn
%O A256173 1,3
%A A256173 _Valtteri Raiko_, Mar 17 2015