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 A222592 #30 Feb 14 2023 23:34:20
%S A222592 5,36,8412,227304,39851304,1622295444,55789710106764
%N A222592 Smallest integer that is a sum of 2*k consecutive primes for each k = 1..n.
%e A222592 a(1) = 5 = 2+3;
%e A222592 a(2) = 36 = 17+19 = 5+7+11+13;
%e A222592 a(3) = 8412 = 4201 + 4211 =
%e A222592 2089 + 2099 + 2111 + 2113 =
%e A222592 1373 + 1381 + 1399 + 1409 + 1423 + 1427;
%e A222592 a(4) = 227304 = 113647 + 113657 =
%e A222592 56813 + 56821 + 56827 + 56843 =
%e A222592 37861 + 37871 + 37879 + 37889 + 37897 + 37907 =
%e A222592 28387 + 28393 + 28403 + 28409 +
%e A222592 28411 + 28429 + 28433 + 28439;
%e A222592 a(5) = 39851304 = 19925627 + 19925677 =
%e A222592 9962809 + 9962819 + 9962837 + 9962839 =
%e A222592 6641839 + 6641851 + 6641867 + 6641891 + 6641903 + 6641953 =
%e A222592 4981367 + 4981373 + 4981387 + 4981393 +
%e A222592 4981423 + 4981441 + 4981451 + 4981469 =
%e A222592 3985063 + 3985067 + 3985073 + 3985087 + 3985099 +
%e A222592 3985103 + 3985181 + 3985207 + 3985211 + 3985213.
%e A222592 The initial primes of the 6 tuples corresponding to a(6) are 811147721, 405573827, 270382529, 202786813, 162229471, and 135191207. - _Giovanni Resta_, Feb 26 2013
%t A222592 a[n_] := Block[{t, w}, t = Table[{Total@(w = Prime@Range@(2*i)), w}, {i, n}]; While[Length@Union[First /@ t] > 1, t = Sort@t; w = NextPrime@t[[1,2,-1]]; t[[1,1]] += w - t[[1,2,1]]; t[[1,2]] = Append[Rest@t[[1,2]], w]]; t[[1,1]]]; Array[a,4] (* _Giovanni Resta_, Feb 26 2013 *)
%Y A222592 Cf. A222564, A288340.
%K A222592 nonn,more
%O A222592 1,1
%A A222592 _Zak Seidov_, Feb 26 2013
%E A222592 a(6) from _Giovanni Resta_, Feb 26 2013
%E A222592 a(7) from _Max Alekseyev_, Feb 12 2023