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 A112527 #13 Nov 22 2019 12:18:22
%S A112527 2,2,5,11,23,43,89,179,359,719,1433,2879,5749,11497,22993,45989,91997,
%T A112527 183971,367949,735901,1471807,2943599,5887213,11774429,23548853,
%U A112527 47097697,94195421,188390809,376781623,753563269,1507126519,3014253049
%N A112527 a(1)=2; a(n)=smallest prime not less than the sum of all previous terms.
%C A112527 See A070218: a(1)=2;a(n)=smallest prime greater than the sum of all previous terms.
%H A112527 Harvey P. Dale, <a href="/A112527/b112527.txt">Table of n, a(n) for n = 1..1000</a>
%t A112527 s={2};ss=2;Do[a=If[PrimeQ[ss], ss, Prime[PrimePi[ss]+1]];AppendTo[s, a];AddTo[ss, a], {i, 35}];A112527=s
%t A112527 Module[{ll={2}},Do[AppendTo[ll,NextPrime[Total[ll]-1]],{40}];ll] (* _Harvey P. Dale_, May 07 2012 *)
%t A112527 nxt[{t_,a_}]:= Module[{c=NextPrime[t-1]}, {t+c,c}]; Rest[NestList[nxt,{0,2},40][[All,2]]] (* _Harvey P. Dale_, Nov 22 2019 *)
%Y A112527 Cf. A070218.
%Y A112527 Cf. A064934. [From _R. J. Mathar_, Aug 15 2008]
%K A112527 easy,nonn
%O A112527 1,1
%A A112527 _Zak Seidov_, Sep 10 2005