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 A038377 #20 Sep 06 2024 16:56:17
%S A038377 1,2,5,11,20,32,47,66,85,110,137,167,200,237,276,320,365,414,467,522,
%T A038377 579,643,708,777,845,924,997,1080,1169,1255,1343,1437,1536,1637,1741,
%U A038377 1847,1961,2075,2187,2311,2435,2560,2691,2826,2962,3104,3249,3393,3543
%N A038377 Number of odd nonprimes <= (2n+1)^2.
%H A038377 Amiram Eldar, <a href="/A038377/b038377.txt">Table of n, a(n) for n = 0..10000</a>
%F A038377 a(n) = A037040(n) + 1.
%F A038377 For n>=1, a(n) = 2n^2 + 2n + 2 - PrimePi((2n+1)^2) = A051890(n+1) - A000720((2n+1)^2). - _Zak Seidov_, Mar 03 2008
%e A038377 a(2) = 5 because there are 5 odd nonprimes that are not exceeding (2*2+1)^2 = 25: 1, 9, 15, 21 and 25.
%t A038377 nn=20001; With[{onps=Complement[Range[1,nn,2],Prime[Range[PrimePi[nn+1]]]]}, Table[Count[onps,_?(#<=(2n+1)^2&)],{n,0,60}]] (* _Harvey P. Dale_, Apr 13 2011 *)
%t A038377 a[n_] := 2*n^2 + 2*n + 2 - PrimePi[(2*n + 1)^2]; a[0] = 1; Array[a, 61, 0] (* _Amiram Eldar_, Sep 06 2024 *)
%o A038377 (PARI) a(n) = if(n == 0, 1, 2*n^2 + 2*n + 2 - primepi((2*n + 1)^2)); \\ _Amiram Eldar_, Sep 06 2024
%Y A038377 Cf. A000720, A037040, A051890.
%K A038377 nonn
%O A038377 0,2
%A A038377 _N. J. A. Sloane_ and _Erich Friedman_
%E A038377 Offset corrected by _Amiram Eldar_, Sep 06 2024