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 A120752 #13 Jan 20 2023 16:13:35
%S A120752 2,3,6,9,10,12,13,16,17,19,20,23,26,27,30,33,34,36,37,40,43,44,47,50,
%T A120752 51,53,54,57,58,60,61,64,67,68,70,71,74,75,77,78,81,84,85,88,91,92,94,
%U A120752 95,98,99,101,102,105,108,109,111,112,115,116,118,119,122,125,126,129,132
%N A120752 Numbers k such that {rk} <= c, where r = (1/2)^(1/2), c = 1/2 and { } denotes fractional part.
%C A120752 Positions of 0 in A083035.
%C A120752 The sequence is essentially identical to A090892 (see links).
%H A120752 Sela Fried, <a href="https://arxiv.org/abs/2301.00644">Equivalent conditions for the nth element of the Beatty sequence B_sqrt(2) being even</a>, arXiv:2301.00644 [math.HO], 2022.
%e A120752 (See A120243.)
%t A120752 r = Sqrt[1/2]; b = 2; c = 0;
%t A120752 f[n_] := Floor[(b*n + c)*r] - b*Floor[n*r] - Floor[c*r];
%t A120752 t = Table[f[n], {n, 1, 200}] (* A083035 *)
%t A120752 Flatten[Position[t, 0]] (* A120752 *)
%t A120752 Flatten[Position[t, 1]] (* A120753 *)
%Y A120752 Cf. A083035, A120753, A190762.
%K A120752 nonn
%O A120752 1,1
%A A120752 _Clark Kimberling_, Jul 01 2006