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 A337573 #17 Feb 06 2021 22:00:13
%S A337573 2,6,26,34,38,60,102,112,116,122,140,230,236,270,300,330,366,386,418,
%T A337573 426,430,486,488,508,530,534,548,556,568,576,600,674,680,688,696,710,
%U A337573 720,764,772,798,802,804,824,852,870,884,906,982,996,1018,1038,1056,1152,1162,1190,1210,1230,1252,1326
%N A337573 Numbers k such that Sum_{i=1..k} prime(i)*prime(k+i) is prime.
%C A337573 All terms are even.
%C A337573 Numbers k such that A337574(k) is prime.
%H A337573 Robert Israel, <a href="/A337573/b337573.txt">Table of n, a(n) for n = 1..8300</a>
%e A337573 a(2)=6 is in the sequence because 2*17 + 3*19 + 5*23 + 7*29 + 11*31 + 13*37 = 1231 is prime.
%p A337573 P:= <seq(ithprime(i),i=1..6000)>:
%p A337573 select(t -> isprime(P[1..t]^%T . P[t+1..2*t]), 2*[$1..1500]);
%t A337573 Select[Range[1326], PrimeQ@ Sum[Prime[i] Prime[# + i], {i, #}] &] (* _Michael De Vlieger_, Sep 01 2020 *)
%Y A337573 Cf. A000040, A337574.
%K A337573 nonn
%O A337573 1,1
%A A337573 _J. M. Bergot_ and _Robert Israel_, Sep 01 2020