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

Terms

a(0) =2a(1) =2a(2) =3a(3) =7a(4) =13a(5) =29a(6) =53a(7) =109a(8) =223a(9) =439a(10) =881a(11) =1759a(12) =3517a(13) =7039a(14) =14071a(15) =28151a(16) =56299a(17) =112601a(18) =225217a(19) =450413a(20) =900821a(21) =1801669a(22) =3603317a(23) =7206631a(24) =14413253a(25) =28826519a(26) =57653027a(27) =115306073a(28) =230612149a(29) =461224289