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 A309265 #30 Aug 09 2019 13:12:01
%S A309265 6,7,8,9,11,12,13,15,16,17,19,21,23,24,25,27,28,29,31,33,35,36,37,39,
%T A309265 40,41,43,45,47,48,49,51,53,55,57,59,60,61,63,64,65,67,69,71,73,75,76,
%U A309265 77,79,81,83,84,85,87,88,89,91,93,95,96,97,99,101,103,105
%N A309265 Numbers k such that s + t = k with 0 < s < t where s and t-s are both prime.
%C A309265 Essentially the same as A210147 with s=p, t-s=q. - _R. J. Mathar_, Aug 09 2019
%e A309265 6 is in the sequence since there are numbers s=2 and t=4 such that s + t = 6 with s < t, and where s=2 and t-s = 4-2 = 2 are both prime.
%e A309265 7 is in the sequence since there are numbers s=3 and t=5 such that s + t = 7 with s < t and where s=3 and t-s = 5-3 = 2 are both prime.
%t A309265 Flatten[Table[If[Sum[(PrimePi[i] - PrimePi[i - 1]) (PrimePi[n - 2 i] - PrimePi[n - 2 i - 1]), {i, Floor[n/2]}] > 0, n, {}], {n, 100}]]
%o A309265 (PARI) isok(k) = {forprime (s=1, k, if (((t = k - s) > s) && isprime(t-s), return (1)););} \\ _Michel Marcus_, Jul 20 2019
%Y A309265 Cf. A309152, A309264.
%K A309265 nonn
%O A309265 1,1
%A A309265 _Wesley Ivan Hurt_, Jul 19 2019