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 A183300 #54 Aug 06 2025 14:53:29
%S A183300 1,3,4,5,6,7,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,
%T A183300 29,30,31,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,51,52,53,
%U A183300 54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,73,74,75,76,77,78,79,80,81,82,83,84,85,86
%N A183300 Positive integers not of the form 2n^2.
%C A183300 Complement of A001105.
%C A183300 Integers whose number of even divisors (A183063) is even (for a proof, see A001105, the complement of this sequence), hence odd numbers (A005408) are a subsequence. - _Bernard Schott_, Sep 15 2021
%H A183300 Bruno Berselli, <a href="/A183300/b183300.txt">Table of n, a(n) for n = 1..1000</a>
%F A183300 a(n) = n + floor(sqrt(n/2) + 1/4). - _Ridouane Oudra_, Jan 26 2023
%F A183300 a(n) = n+m+1 if n>(m+1)*(2m+1) and a(n) = n+m otherwise where m = floor(sqrt(n/2)). - _Chai Wah Wu_, Aug 04 2025
%e A183300 10 is in the sequence since 2*2^2=8 < 10 < 2*3^2=18.
%p A183300 A183300:=n->if type(sqrt(2*n)/2, integer) then NULL; else n; fi; seq(A183300(n), n=1..100); # _Wesley Ivan Hurt_, Dec 17 2013
%t A183300 a = 2; b = 0;
%t A183300 F[n_] := a*n^2 + b*n;
%t A183300 R[n_] := (n/a + ((b - 1)/(2a))^2)^(1/2);
%t A183300 G[n_] := n - 1 + Ceiling[R[n] - (b - 1)/(2a)];
%t A183300 Table[F[n], {n, 60}]
%t A183300 Table[G[n], {n, 100}] (* _Clark Kimberling_ *)
%t A183300 r[n_] := Reduce[n == 2*k^2, k, Integers]; Select[Range[100], r[#] === False &] (* _Jean-François Alcover_, Dec 17 2013 *)
%t A183300 max = 100; Complement[Range[max], 2 Range[Ceiling[Sqrt[max/2]]]^2] (* _Alonso del Arte_, Dec 17 2013 *)
%t A183300 Module[{nn=10,f},Complement[Range[2nn^2],2Range[nn]^2]] (* _Harvey P. Dale_, Sep 06 2023 *)
%o A183300 (Magma) [n: n in [0..100] | not IsSquare(n/2)]; // _Bruno Berselli_, Dec 17 2013
%o A183300 (PARI) is(n)=!issquare(n/2) \\ _Charles R Greathouse IV_, Sep 02 2015
%o A183300 (PARI) a(n)=my(k=sqrtint(n\2)+n); if(k-sqrtint(k\2)<n,k+1,k) \\ _Charles R Greathouse IV_, Sep 02 2015
%o A183300 (Python)
%o A183300 from math import isqrt
%o A183300 def A183300(n): return n+(m:=isqrt(n>>1))+(n>(m+1)*((m<<1)+1)) # _Chai Wah Wu_, Aug 04 2025
%Y A183300 Cf. A005408, A183063.
%Y A183300 Cf. A001105 (number of even divisors is odd), A028982 (number of odd divisors is odd), A028983 (number of odd divisors is even), this sequence (number of even divisors is even).
%K A183300 nonn,easy
%O A183300 1,2
%A A183300 _Clark Kimberling_, Jan 03 2011
%E A183300 Name clarified by _Wesley Ivan Hurt_, Dec 17 2013