a(1)=2; a(n)=smallest prime greater than the half-sum of all previous terms.

Terms

a(0) =2a(1) =2a(2) =3a(3) =5a(4) =7a(5) =11a(6) =17a(7) =29a(8) =41a(9) =59a(10) =89a(11) =137a(12) =211a(13) =307a(14) =461a(15) =691a(16) =1039a(17) =1559a(18) =2339a(19) =3511a(20) =5261a(21) =7901a(22) =11863a(23) =17783a(24) =26669a(25) =40009a(26) =60013a(27) =90011a(28) =135017a(29) =202529