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