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%I #9 Jun 17 2012 02:17:05
%S 2,2,3,7,13,29,53,109,223,439,881,1759,3517,7039,14071,28151,56299,
%T 112601,225217,450413,900821,1801669,3603317,7206631,14413253,
%U 28826519,57653027,115306073,230612149,461224289,922448587,1844897167,3689794321
%N Slowest increasing sequence in which a(n) is a prime closest to the sum of all previous terms.
%C Cf. A109278 fastest increasing sequence in which a(n) is a prime closest to the sum of all previous terms.
%e a(1)=2, sum(1)=2; prime closest to sum is 2, hence a(2)=2, sum(2)=4; there are two primes 3 and 5 closest to sum(2), we choose the smallest one, hence a(3)=3, sum(3)=7, etc.
%t s={2};su=2;Do[If[PrimeQ[su], a=su, pp=PrimePi[su];prv=Prime[pp];nxt=Prime[pp+1];a=If[su-prv>nxt-su, nxt, prv]];AppendTo[s, a];Print[a];su+=a, {i, 42}];s
%Y Cf. A109278.
%K nonn
%O 1,1
%A _Zak Seidov_, Jun 25 2005
%E Definition and comment clarified by _Jonathan Sondow_, Jun 16 2012