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

Terms

a(0) =2a(1) =2a(2) =5a(3) =11a(4) =19a(5) =41a(6) =79a(7) =157a(8) =317a(9) =631a(10) =1259a(11) =2521a(12) =5039a(13) =10079a(14) =20161a(15) =40343a(16) =80669a(17) =161333a(18) =322669a(19) =645329a(20) =1290673a(21) =2581349a(22) =5162681a(23) =10325369a(24) =20650753a(25) =41301493a(26) =82602997a(27) =165205981a(28) =330411959a(29) =660823921