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 A273457 #30 Dec 24 2016 11:28:17
%S A273457 2,4,6,8,12,18,20,22,24,26,30,32,38,40,44,52,56,58,62,64,70,72,76,82,
%T A273457 84,88,92,94,98,100,102,104,106,108,110,112,114,116,118,120,122,126,
%U A273457 128,130,132,134,136,140,144,146,152,154,156,158,164,166,172,182,188,196,198,200,214
%N A273457 Even numbers 2n that do not have a Goldbach partition 2n = p + q (p < q; p, q prime) satisfying sqrt(n) < p <= sqrt(2n).
%C A273457 This is an extension of A244408.
%C A273457 There are 74 elements of A279040 that are also in this sequence. These common elements are in A244408.
%C A273457 It is conjectured that a(12831) = 15702604 is the last term. There are no more terms below 4*10^10.
%H A273457 Corinna Regina Böger, <a href="/A273457/b273457.txt">Table of n, a(n) for n = 1..12831</a>
%e A273457 32 is in the sequence because 32 has two Goldbach partitions: 32 = 3 + 29 with 3 < sqrt(16) and 32 = 13 + 19 with 13 > sqrt(32).
%t A273457 noGoldbatSqrQ[n_] := Block[{p = NextPrime[Sqrt[n/2]]}, While[2p < n && !PrimeQ[n - p], p = NextPrime@ p]; p > Sqrt[n]]; noGoldbatSqrQ[4] = True; Select[2Range[107], noGoldbatSqrQ] (* _Robert G. Wilson v_, Dec 15 2016 *)
%o A273457 (PARI) noSpecialGoldbach(n) = forprime(p=sqrtint(n/2-1) + 1, sqrtint(n), if(p<(n-p) && isprime(n-p), return(0))); 1
%o A273457 is(n) = n%2 == 0 && noSpecialGoldbach(n)
%Y A273457 Cf. A002373, A020481, A025018, A025019, A244408, A279040.
%K A273457 nonn
%O A273457 1,1
%A A273457 _Corinna Regina Böger_, Dec 11 2016