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 A098042 #20 Jul 08 2024 08:53:15
%S A098042 307,593,1459,1511,1609,2399,2447,2579,2903,4409,5953,6317,7151,11083,
%T A098042 12491,14753,16067,18199,18223,20929,21787,23893,25667,26317,31051,
%U A098042 37139,37573,37871,40283,40471,41201,41479,42013,44537,44741,48409
%N A098042 Primes of the form (prime(prime(k)) + prime(prime(k+1)))/2.
%C A098042 Primes of the form A299644(k)/2. - _Amiram Eldar_, Jul 08 2024
%H A098042 Amiram Eldar, <a href="/A098042/b098042.txt">Table of n, a(n) for n = 1..10000</a>
%e A098042 prime(prime(18)) = 283, prime(prime(19)) = 331. (283 + 331)/2 = 614/2 = 307.
%t A098042 With[{t = Table[Prime[Prime[n]], {n, 1, 400}]}, Select[(Most[t] + Rest[t])/2, PrimeQ]] (* _Amiram Eldar_, Jul 08 2024 *)
%o A098042 (PARI) lista(n) = for(x=1,n,y=prime(prime(x+1))+prime(prime(x)); if(y%2==0&isprime(y/2),print1(y\2",")))
%Y A098042 Cf. A006450, A098043, A299644.
%K A098042 easy,nonn
%O A098042 1,1
%A A098042 _Cino Hilliard_, Sep 10 2004
%E A098042 Offset corrected by _Amiram Eldar_, Jul 08 2024