a(1) = 7; for n > 1, a(n) = smallest prime strictly greater than sum of previous terms.

Terms

a(0) =7a(1) =11a(2) =19a(3) =41a(4) =79a(5) =163a(6) =331a(7) =653a(8) =1307a(9) =2617a(10) =5231a(11) =10463a(12) =20929a(13) =41863a(14) =83717a(15) =167437a(16) =334877a(17) =669763a(18) =1339523a(19) =2679037a(20) =5358083a(21) =10716163a(22) =21432317a(23) =42864671a(24) =85729367a(25) =171458671a(26) =342917357a(27) =685834729a(28) =1371669443a(29) =2743338881