A109278 - OEIS

%I #9 Jun 17 2012 02:17:18

%S 2,2,5,11,19,41,79,157,317,631,1259,2521,5039,10079,20161,40343,80669,

%T 161333,322669,645329,1290673,2581349,5162681,10325369,20650753,

%U 41301493,82602997,165205981,330411959,660823921,1321647869,2643295709

%N Fastest increasing sequence in which a(n) is a prime closest to the sum of all previous terms.

%C A109277 is the slowest 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 largest one, hence a(3)=5, 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, prv, nxt]];AppendTo[s, a];Print[a];su+=a, {i, 42}];s

%Y Cf. A109277.

%K nonn

%O 1,1

%A _Zak Seidov_, Jun 25 2005

%E Definition and comment clarified by _Jonathan Sondow_, Jun 16 2012