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 A070805 #7 Jun 21 2020 11:36:06
%S A070805 2,3,5,7,17,31,61,113,239,467,941,1879,3761,7523,15031,30071,60149,
%T A070805 120299,240599,481181,962363,1924721,3849437,7698893,15397783,
%U A070805 30795571,61591147,123182281,246364571,492729101,985458239,1970916449
%N A070805 a(1) = 2; a(n) = largest prime not exceeding the sum of all previous terms.
%t A070805 tb[0]={} tb[x_] := Union[tb[x-1], m[x]] m[x_] := {Prime[PrimePi[Apply[Plus, tb[x-1]]]]} Union[Delete[Flatten[Table[m[w], {w, 1, 20}]], 1], {2}]
%t A070805 nxt[{t_,p_}]:=Module[{c=If[PrimeQ[t],t,NextPrime[t,-1]]},{t+c,c}]; Join[ {2},NestList[nxt,{5,3},40][[All,2]]] (* _Harvey P. Dale_, Jun 21 2020 *)
%Y A070805 Cf. A070218.
%K A070805 nonn
%O A070805 1,1
%A A070805 _Labos Elemer_, May 08 2002