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 A258834 #32 Mar 02 2025 10:10:24
%S A258834 0,3,6,10,13,17,20,24,27,30,34,37,41,44,47,51,54,58,61,65,68,71,75,78,
%T A258834 82,85,88,92,95,99,102,105,109,112,116,119,123,126,129,133,136,140,
%U A258834 143,146,150,153,157,160,164,167,170,174,177,181,184,187,191,194
%N A258834 Nonhomogeneous Beatty sequence: a(n) = ceiling((n - 1/4)*(2 + sqrt(2))).
%C A258834 Complement of A258833.
%C A258834 See A258833 for more comments.
%H A258834 Clark Kimberling, <a href="/A258834/b258834.txt">Table of n, a(n) for n = 0..10000</a>
%H A258834 Aviezri S. Fraenkel, <a href="http://dx.doi.org/10.4153/CJM-1969-002-7">The bracket function and complementary sets of integers</a>, Canadian J. of Math. 21 (1969) 6-27.
%H A258834 Clark Kimberling, <a href="https://www.emis.de/journals/INTEGERS/papers/q15/q15.Abstract.html">Beatty sequences and trigonometric functions</a>, Integers 16 (2016), #A15.
%F A258834 a(n) = ceiling((n - 1/4)*(2 + sqrt(2))) = floor((n - 1/4)*(2 + sqrt(2)) + 1).
%t A258834 r = Sqrt[2]; s = r/(r - 1);
%t A258834 Table[Ceiling[(n + 1/4) r], {n, 0, 100}] (* A258833 *)
%t A258834 Table[Ceiling[(n - 1/4) s], {n, 0, 100}] (* A258834 *)
%o A258834 (Magma) [Ceiling((n-1/4)*(2+Sqrt(2))): n in [0..80]]; // _Vincenzo Librandi_, Jun 13 2015
%o A258834 (PARI) vector(60, n, ceil((n-1/4)*(2+sqrt(2)))) \\ _G. C. Greubel_, Aug 19 2018
%Y A258834 Cf. A258833 (complement), A184580, A184581.
%K A258834 nonn,easy
%O A258834 0,2
%A A258834 _Clark Kimberling_, Jun 12 2015
%E A258834 Corrected by _Michel Dekking_, Sep 19 2019